Decimals CHAPTER 8 Introduction A part of a whole can be expressed in decimal or decimals are another way of representing fractions. In earlier classes, we learnt that dot represents a decimal point. Now, we shall learn more about decimals. To Read a Decimal Number A decimal or a decimal number contains a whole number part and a decimal number part separated by a dot (.) For example : In 36.47, 36 is the whole part and 47 is the decimal part. Write the following decimal numbers as number names. (i) 34.6 (ii) 4.778 (iii) 872.4 (iv) 26.346 Soln.: (i) 34.6 Thirty four point five six. (ii) 4.778 Four point seven seven eight. (iii) 872.4 Eight hundred seventy two point one four (iv) 26.346 Twenty six point three four six. Decimal Fractions The fractions in which the denominators are 0,00, 000, etc..., are known as decimal fractions. Place value of decimal numbers In the whole number part, if we move right to left by place, the value of a digit increases by 0 times for each place. In the decimal part, if we move left to right by place, the value of a digit decreases by for each place. 0 See the following place value chart for 463.427, 879.34 and 6284.932. Thousands 000 Hundreds 00 Tens 0 Ones Decimal point Tenths 0 Hundredths 00 Thousandths 000 4 6 3. 4 2 7 8 7 9. 3 4 6 2 8 4. 9 3 2 Tenths place If we move one place to the right of ones place, the place value becomes of the digit and this place is known as tenths place. 0 For example : Place value of 6 in 43.628 is 6 0. DECIMALS 39
Hundredths place If we move one place to the right of tenths place, the place value becomes of the digit and this place is known as hundredths place. 00 For example : Place value of 2 in 43.628 is 2 00. Thousandths place If we move one place to the right of hundredths place, the place value becomes of the digit and this place is known as thousandths place. 000 8 For example : Place value of 8 in 43.628 is 000. 2 Find the place value of 6, 9 and 4 in 38.694. Soln.: Place value of 6 is 6 0 Place value of 9 is 9 00 4 Place value of 4 is 000 3 Find the place value of following in the number 829.43. (i) 4 (ii) 3 (iii) Soln.: (i) Place value of 4 is 4 0 (ii) Place value of 3 is 3 00 (iii) Place value of is 000 Expanded form In 342.697, the place values are given as 3 4 2. 6 9 7 7 or 0.007 000 3 000 or 3000 00 or 00 9 or 0.09 00 4 0 or 40 2 6 or 0.6 0 342.697 can be written as 3000 + 00 + 40 + 2 + 6 0 + 9 00 + 7. This is known as expanded form of 000 a decimal number. 4 Write the following in numeral form. (i) Twenty and five-tenths. (ii) Five ones, two-tenths and four-hundredths. (iii) Three hundred two ones and six hundredths. (iv) Two ones and eight thousandths. Soln.: (i) 20 + 0 = 20. (ii) + 2 0 + 4 00 =.24 6 (iii) 300 + 2 + 00 = 302.06 8 (iv) 2 + 000 = 2.008 40 DECIMALS Class 6 Mathematics
Write the following as decimals: (i) (ii) Tens Ones Tenths Hundreds block Tens Ones (iii) 20 + + 9 0 + 6 000 Soln.: (i) In 40 + 2 + 6 0 We have 4 tens, 2 ones and 6 tenths Decimal is 42.6. (ii) In 800 + 20 + 8 0 + 4, we have 8 hundreds, 00 2 tens, 8 tenths and 4 hundredths. Decimal is 820.84 (iii) In 20 + + 9 0 + 6, we have 2 tens, ones, 000 9 tenths and 6 thousandths Decimal is 2.906. 7 Give a decimal for the number of shaded squares. (i) (ii) Tenths Hundredths Soln.: (i) 30 + 2 + 2 0 = 32.2 (ii) 00 + 20 + 4 + 2 0 + 4 00 = 24.24 6 Write the following as decimals. (i) 40 + 2 + 6 0 (ii) 800 + 20 + 8 0 + 4 00 Soln.: (i) 60 parts are shaded out of 00 parts i.e., 60 00 = 0.6 (ii) 4 parts are shaded out of 00 parts i.e., 4 00 = 0.04 Representing Decimals on Number Line Let us try to represent 0.8 on a number line. We know that 0.8 is greater than 0 but less than. So we divide the numbers from 0 to into 0 equal parts on number line and name it as 0., 0.2, and so on till.0. 0 0. 0.2 0.3 0.4 0. 0.6 0.7 0.8 0.9..2.3.4..6.7.8.9 2 Similarly, if we had to place 0.08, we further divide 0.0 to 0. into 0 equal parts and name it as 0.0, 0.02 and so on till 0.0. 0 0.0 0.02 0.03 0.04 0.0 0.06 0.07 0.08 0.09 0. 0. 0.2 0.3 0.4 0. 0.6 0.7 0.8 0.9 0.2 8 Find the values of P, Q, R, S and T on the given number line. P T Q R S 0 2 3 4 Soln.: P = 0.7, Q = 2.4, R = 3.2, S = 4.9 and T =.3 DECIMALS 4
Comparing Decimals First, compare the whole numbers to the left of the decimal point. If they are not the same, the smaller decimal number is the one with the smaller whole numbers. On the other hand, if they are the same, compare the whole number to the right of the decimal point. We start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc, until one decimal is larger. Like and unlike decimals z Decimals having equal number of digits to the right of the decimal point are known as like decimals. For example:.23 and 6.498 z Decimals not having equal number of digits to the right of the decimal point are known as unlike decimals. For example: 6.92 and 8.32. Converting unlike decimals into like decimals We can convert unlike decimals into like decimals by adding zeroes to the right of decimal point. 9 Which decimal is greater? (i) 82.23 or 68.2 (ii) 0.432 or 0.98 (iii) 32.064 or 32.0 Soln.: (i) 82.23 or 68.2 Since, whole parts of both the numbers are different. So, 82.23 > 68.2 (ii) 0.432 or 0.98 Since, whole parts of both the numbers are same. So, we compare tenths parts. Hence, 0.98 > 0.432 (iii) 32.064 or 32.0 Since, whole parts of both the numbers are same. So, we compare tenths parts. But tenths parts are also same. So, we compare hundredths parts. Hence, 32.064 > 32.0 0 Convert 8., 4.32 and 7.69 into like decimals. Soln.: 8. = 8.00, 4.32 = 4.320 and 7.69 = 7.69 Hence, 8.00, 4.320 and 7.69 are like decimals. Arrange the following in ascending order. 32.43, 32.336, 32, 32.003, 32.3 Soln.: Depending on their place value, we can arrange them in ascending order as 32, 32.003, 32.3, 32.336, 32.43. 2 Arrange the following in descending order. 6.6, 6.604, 6.064, 6, 6.664 Soln.: Depending on their place value, we can arrange them in descending order as 6.664, 6.604, 6.6, 6.064, 6. Conversion of fractions into decimals Step : Find a number you can multiply by the bottom of the fraction to make it 0, or 00, or 000, or any followed by 0s. Step 2 : Multiply both top and bottom by that number. Step 3 : Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number.) 42 DECIMALS Class 6 Mathematics
3 Convert the following fractions into decimals. 3 3 2 (i) (ii) (iii) 4 2 Soln.: (i) 3 Multiply the numerator and denominator by 2 to make denominator as 0 3 2 2 = 26 0 = 2.6 3 = 2.6 (ii) 3 4 Multiply the numerator and denominator by 2 to make denominator 00. 3 4 2 2 = 7 00 = 0.7 (iii) 2 2 Multiply the numerator and denominator by to make denominator 0. 2 2 = 2 0 = 2. 2 2 = 2. Conversion of decimals into fractions Step : Write down the decimal divided by, like this: Decimal Step 2 : Multiply both top and bottom by 0 for every digit after the decimal point. (For example, if there are two digits after the decimal point, then use 00, if there are three then use 000, etc.) Step 3 : Simplify (or reduce) the fraction. 4 Convert the following decimals into fractions. (i) 0.06 (ii) 9.64 (iii) 7.2 Soln.: (i) 0.06 = 0.06 Since, there are two digits after decimal point, so we multiply both top & bottom by 00. 0.06 00 00 = 6 00 = 3 0 Hence, 0.06 = 3 0 (ii) 9.64 = 9.64 Since, there are three digits after decimal point, so, we multiply both top & bottom by 000. 9.64 000 000 = 964 000 = 929 200 Hence, 9.64 = 929 200 (iii) 7.2 = 7.2 Since, there is one digit after decimal point, so we multiply both top & bottom by 0. 7.2 0 0 = 72 0 = 36 Hence, 7.2 = 36 Use of Decimals Money We know that, 00 paise = ` paise = ` 00 = ` 0.0 Length We know that, 00 cm = m cm = 00 m = 0.0 m Similarly, 000 m = km DECIMALS 43
Weight We know that, 000 g = kg g = kg = 0.00 kg 000 Convert the following into rupees. (i) 60 paise (ii) 0 rupees 80 paise Soln.: (i) paise = ` 00 So, 60 paise = ` 60 00 = `.60 80 (ii) paise = `, 80 paise = ` 00 00 = ` 0.80 So, 0 rupees 80 paise = ` 0 + ` 0.80 = ` 0.80 6 Convert the following as instructed. (i) 2004 cm into m (ii) 8 km 42 m into km (iii) 428 mm into cm Soln.: (i) cm = 00 m So, 2004 cm = 2004 00 m = 20.04 m (ii) m = 000 km 42 m = 42 km = 0.042 km 000 So, 8 km 42 m = 8 km + 0.042 km = 8.042 km (iii) mm = 0 cm So, 428 mm = 428 cm = 42.8 cm 0 7 Convert the following into kg. (i) 3840 g (ii) 2 kg 0 g Soln.: (i) g = 000 kg So, 3840 g = 3840 kg = 3.840 kg 000 (ii) g = 000 kg 0 g = 0 kg = 0.00 kg 000 So, 2 kg 0 g = 2 kg + 0.00 kg = 2.00 kg Addition of decimals To add the decimals, we proceed as following: z Convert the given decimals into like decimals. z Write one number below the other so that the bottom decimal point is directly below and lined up with the top decimal point. z Then add using column addition, remembering to put the decimal point in the answer. 8 Add the following decimals. (i) 2.237 + 0.23 +.664 (ii) 9.76 +.66 (iii) 2.3667 + 2.7 + 3.22 Soln.: (i) 2. 2 3 7 0 0. 2 3 +. 6 6 4 8. 0 4 7 (ii) 9. 7 6 +. 6 6 0 0. 8 3 6 (iii) 2. 3 6 6 7 2. 7 0 0 + 3. 2 2 0 0 8. 6 7 9 Bala has ` 69.24. His father gave him ` 00.48 and his mother gave ` 0.40. How much amount he has? Soln.: Amount of money Bala has = ` 69.24 Amount of money his father gave = ` 00.48 Amount of money his mother gave = ` 0.40 Total money Bala has = ` 69.24 + ` 00.48 + ` 0.40 = ` 220.2 44 DECIMALS Class 6 Mathematics
Subtraction of Decimals To subtract the decimals, we proceed as follows: z Convert the given decimals into like decimals. z Write one number below the other so that the bottom decimal point is directly below and lined up with the top decimal point. z Then subtract normally, remembering to put the decimal point in the answer. 20 Solve: (i) Subtract.7609 from 6.93 (ii) Subtract 8.6 from 9.9603 (iii) Subtract 2.836 from 3.22 Soln.: (i) 6. 9 3 0. 7 6 0 9. 7 4 (ii) 9. 9 6 0 3 8. 6 0 0. 3 0 3 (iii) 3. 2 2 0 0 2. 8 3 6 0. 3 6 6 4 2 Priya bought.2 kg of rice. She consumed.73 kg of rice. How much rice remains with her? Soln.: Quantity of rice Priya bought =.2 kg Quantity of rice she consumed =.73 kg Quantity of rice left with her =.2 kg.73 kg = 3.2 kg DECIMALS 4
z A decimal has two parts - Whole number part and Decimal part. z The fractions in which the denominators are 0, 00, 000 etc. are known as decimal fractions. z Decimals having the same number of decimal places are called like decimals, otherwise they are unlike decimals. z To convert a decimal into a fraction, write the figure without the decimal point as the numerator of the fraction. In the denominator write followed by as many zeroes as there are decimal places in the given decimal. z Zero to the extreme right of the decimal number does not have any value. z To add or subtract any two or more decimal numbers, it is better to change them into like decimals and then do the required operation of numbers. 46 DECIMALS Class 6 Mathematics
SOLVED EXAMPLES. Write the following numbers in the place value chart (table). (i) 42.76 (ii) 32.34 (iii) 763.42 Soln.: Number Thousands Hundreds Tens Ones Decimal Tenths Hundredths Thousandths (i) 42.76 4 2. 7 6 (ii) 32.34 3 2. 3 4 (iii) 763.42 7 6 3. 4 2 2. Write each of the following as a decimal. (i) Two hundred five and three hundredths (ii) Thirteen point one two three (iii) Eight and thirty five thousandths Soln.: (i) Two hundred five and three hundredths 3 = 20 + 00 = 2 00 + 0 0 + + 0 0 + 3 00 = 20.03 (ii) Thirteen point one two three = 3.23 (iii) Eight and thirty five thousandths 3 = 8 + 000 = 8 + 30 + 000 = 8 + 30 000 + 000 = 8 + 0 0 + 3 00 + 000 = 8.03 3. Sundaram bought a toothpaste for ` 8.7, soap for ` 6 and shoe polish for ` 2.0. He gave a fifty rupee note to the shopkeeper. Find the money he got back. Soln.: Cost of the toothpaste = Cost of the soap = Cost of the shoe polish = Total expenditure = ` 8. 7 ` 6. 0 0 +` 2. 0 ` 3 7. 2 Money he got back = ` 0 37.2 = ` 2.7 4. Write the decimal numbers represented by the points A, B and C on the number line. A B C 0 2 3 4 Soln.: A =., B = 2.7, C = 3.. Compare the following. (i) 63.84 and 7.98 (ii) 27.04 and 27.0 (iii) 82.438 and 82.434 (iv) 9.09 and 9.2 Soln.: (i) 63.84 > 7.98 (ii) 27.04 < 27.0 (iii) 82.438 > 82.434 (iv) 9.09 < 9.2 6. Write each of the following as decimals. (i) 300 + 60 + 9 + 0 + 8 00 (ii) 700 + 9 + 2 0 + 6 000 (iii) 8 0 + 00 + 4 000 (iv) 20 + 4 + 00 Soln.: (i) 300 + 60 + 9 + 0 + 8 00 = 369.8 (ii) 700 + 9 + 2 0 + 6 000 = 709.206 (iii) 8 0 + 00 + 4 000 = 0.84 (iv) 20 + 4 + 00 = 24.0 7. Using decimals, express: (i) 0 cm 6 mm as cm (ii) 08 cm as m (iii) `,40 paise as rupees (iv) ` 0,8 paise as rupees Soln.: (i) 0 cm 6 mm = 0 cm + 6 0 cm = 00 cm + 6 cm 0 = 06 0 (ii) 08 cm = 08 00 m =.08 m cm = 0.6 cm (iii) ` + 40 paise = ` + ` 40 00 ` 00 + ` 40 = = ` 40 00 00 = `.40 (iv) ` 0 + 8 paise = ` 0 + ` 8 = ` 000 + ` 8 00 00 = ` 08 00 = ` 0.8 8. Shweta travelled 2 km 220 m by bus, 8 km 48 m by car and the rest 760 m she walked. How much distance did she travel in all? Soln.: Distance travelled by bus = 2 km 220 m = 2.220 km Distance travelled by car = 8 km 48 m = 8.48 km Distance travelled by walking = 760 m = 0.760 km Therefore, total distance travelled is = 2.220 km + 8.48 km + 0.760 km = 2.46 km Hence, Shweta travelled 2.46 km in all. DECIMALS 47
9. Write the following decimals in expanded form. (i) 2.7 (ii) 42.344 (iii) 76.08 (iv) 63.704 Soln.: (i) 2.7 = 2 + 7 0 + 00 (ii) 42.344 = 00 + 40 + 2 + 3 0 + 4 (iii) 76.08 = 70 + 6 + 8 00 00 + 4 000 (iv) 63.704 = 000 + 00 + 60 + 3 + 7 0 + 4 000 0. Convert the following fractions into decimals. 8 (i) (ii) 22 000 20 (iii) 4 Soln.: (i) 8 000 = 0.08 (iv) 77 2 (ii) 22 20 = 22 4 20 4 = 848 000 = 0.848 (iii) 4 = 4 2 2 = 8 0 = 0.8 (iv) 77 2 = 77 4 2 4 = 308 00 = 3.08. Convert the following decimals into fractions. (i) 20.04 (ii) 9.43 (iii).02 (iv) 0.7 Soln.: (i) 20.04 = 20.04 (ii) 9.43 = 9.43 00 00 = 2004 00 = 300 2 000 000 = 943 000 = 887 200 (iii).02 =.02 000 000 = 02 000 = 373 20 (iv) 0.7 = 0.7 00 00 = 7 00 = 3 4 2. Tanuj walked 8.62 km on Monday, 7.0 km on Tuesday and some distance on Wednesday. If he walked 20 m in three days, how much distance did he walk on Wednesday? Soln.: Distance walked by Tanuj on Monday = 8.62 km Distance walked by Tanuj on Tuesday = 7.0 km Distance walked by Tanuj on Monday and Tuesday = 8.62 km + 7.0 km =.67 km =.670 km Distance walked by Tanuj on Monday, Tuesday and Wednesday = 20 m = 20 km = 2.0 km 000 Distance walked by Tanuj on Wednesday = 2.0 km.670 km =.34 km 3. Give a decimal for the number of shaded squares. (i) (ii) (iii) Soln.: (i) 7 parts are shaded out of 00 parts. i.e., 7 00 = 0.7 (ii) 40 parts are shaded out of 00 parts i.e., 40 00 = 0.40 (iii) 8 parts are shaded out of 00 parts i.e., 8 00 = 0.8 4. Write the place value of 6 in the following decimal numbers. (i) 28.63 (ii).6 (iii) 8.036 Soln.: (i) Place value of 6 in 28.63 is 6 0. (ii) Place value of 6 in.6 is 6 00. 6 (iii) Place value of 6 in 8.036 is 000.. Write the following as numbers. (i) (ii) Tens Ones Tenths Hundreds Tens Tenths Soln.: (i) 30 + + 6 0 = 3.6 (ii) 00 + 0 + 4 0 = 0.4 48 DECIMALS Class 6 Mathematics
NCERT SECTION Exercise 8.. Write the following as numbers in the given table. (a) (b) Hundreds (00) Tens Ones Tenths Hundreds Tens Tenths Soln.: Hundreds (00) Tens (0) Tens (0) Ones () Ones () Tenths 0 Tenths 0 (a) 0 3 2 (b) 0 4 2. Write the following decimals in the place value table. (a) 9.4 (b) 0.3 (c) 0.6 (d) 20.9 Soln.: (a) Hundreds Tens Ones Tenths 0 9 4 (b) Hundreds Tens Ones Tenths 0 0 0 3 (c) Hundreds Tens Ones Tenths 0 0 6 (d) Hundreds Tens Ones Tenths 2 0 9 3. Write each of the following as decimals : (a) Seven-tenths (b) Two tens and nine-tenths (c) Fourteen point six (d) One hundred and two ones (e) Six hundred point eight 7 Soln.: (a) Seven-tenths = 7 tenths = = 07. 0 (b) Two tens and nine-tenths = 2 0 + 9 0 = 20 + 0.9 = 20.9 (c) Fourteen point six = 4.6 (d) One hundred and two-ones = 00 + 2 = 00 + 2 = 02.0 (e) Six hundred point eight = 600.8 4. Write each of the following as decimals: (a) 0 (c) 200 + 60 + + (e) (g) (i) 88 0 3 2 2 (b) 3 + 7 0 0 (d) 70 8 + 0 (f) 4 2 (h) 2 0 (j) 3 3 (k) 4 2 7 Soln.: (a) = 0. (b) 3+ = 3+ 0. 7 = 37. 0 0 (c) 200 + 60 + + = 200 + 60 + + 0. = 26. 0 8 (d) 70 + = 70 + 08. = 70. 8 0 (e) 88 80 + 8 80 8 8 = = + = 8 + = 8 + 08. = 88. 0 0 0 0 0 (f) 4 2 2 = 4 + = 4+ 0. 2= 4. 2 0 0 (g) 3 3 0 0 = 0 2 2 = 0 = + = + = +. =. 0 0 0 (h) 2 2 2 4 = 04 2 = 0 =. (i) 2 2 2 24 20 + 4 20 4 = = = = + = 2 + 04. = 2. 4 2 0 0 0 0 (j) 3 3 3 3 3 3 2 6 = + = + 3 3 06 3 6 2 0 (k) 4 4 4 = + = + 4 4 0 4 2 2 2 0. Write the following decimals as fractions. Reduce the fractions to lowest form. (a) 0.6 (b) 2. (c).0 (d) 3.8 (e) 3.7 (f) 2.2 (g) 6.4 DECIMALS 49
6 Soln.: (a) 06. = 3 0 = (b) 2 2. = = 0 2 0 38 9 (c) 0. = = (d) 38. = = 0 0 37 22 06 (e) 37. = (f) 2. 2 = = 0 0 64 (g) 64. = = 0 32 6. Express the following as cm using decimals. (a) 2 mm (b) 30 mm (c) 6 mm (d) 4 cm 2 mm (e) 62 mm (f) 83 mm Soln.: (a) Q 0 mm = cm \ mm = cm 0 \ 2 mm = 2cm = 02. cm 0 (b) Q 0 mm = cm \ mm = cm 0 \ 30 mm = 30 cm = 30. cm 0 (c) Q 0 mm = cm \ mm = cm 0 \ 6 mm = 6 cm =. 6 cm 0 (d) Q 0 mm = cm 2 \ 4cm+ cm = (4 + 0.2) cm = 4.2 cm 0 (e) Q 0 mm = cm \ mm = cm 0 \ 62 mm = 62 cm = 6. 2 cm 0 (f) Q 0 mm = cm \ mm = cm 0 \ 83 mm = 83 cm = 83. cm 0 7. Between which two whole numbers on the number line are the given numbers lie? Which of these whole numbers is nearer the number? 0 2 3 4 6 7 8 9 0 2 (a) 0.8 (b). (c) 2.6 (d) 6.4 (e) 9. (f) 4.9 Soln.: (a) 0.8 lies between 0 and. From 0 to, 0.8 is nearer to. (b). lies between and 6. From to 6,. is nearer to. (c) 2.6 lies between 2 and 3. From 2 to 3, 2.6 is nearer to 3. (d) 6.4 lies between 6 and 7. From 6 to 7, 6.4 is nearer to 6. (e) 9. lies between 9 and 0. From 9 to 0, 9. is nearer to 9. (f) 4.9 lies between 4 and. From 4 to, 4.9 is nearer to. 8. Show the following numbers on the number line. (a) 0.2 (b).9 (c). (d) 2. Soln.: (a) 0.2 (c). (b).9 (d) 2. 0 2 3 9. Write the decimal number represented by the points A, B, C, D on the given number line. 0 A B 2 C D3 8 3 Soln.: A = 0 + = 08., B = + = 0 0 2 9 C = 2 + = 22., D = 2 + = 0 0 3., 29. 0. (a) The length of Ramesh s notebook is 9 cm mm. What will be its length in cm? (b) The length of a young gram plant is 6 mm. Express its length in cm. Soln.: (a) 9 cm mm = 9 cm + mm = 9 + 0 cm = 9. cm 6 (b) 6mm= cm = 6. cm 0 Exercise 8.2. Complete the table with the help of these boxes and use decimals to write the number. (a) (b) (c) Ones Tenths Hundredths Number (a) (b) (c) Soln.: Ones Tenths Hundredths Number (a) 0 2 6 0.26 (b) 3 8.38 (c) 2 8.28 4 0 DECIMALS Class 6 Mathematics
2. Write the numbers given in the following place value table in decimal form. Hundreds 00 Tens 0 Ones Tenths 0 Hundredths 00 Thousandths 000 (a) 0 0 3 2 0 (b) 0 2 6 3 0 (c) 0 3 0 0 2 (d) 2 9 0 2 (e) 0 2 2 4 Soln.: (a) 0 00 + 0 0 + 3 + 2 + + 0 0 00 = 0 + 0 + 3 + 0.2 + 0.0 + 0 = 3.2 (b) 00 + 0 0 + 2 + 6 0 + 3 + 0 00 = 00 + 0 + 2 + 0.6 + 0.03 + 0 = 02.63 (c) 0 00 + 3 0 + 0 + 0 0 + 000 000 + 2 + 00 000 = 0 + 30 + 0 + 0 + 0.02 + 0.00 = 30.02 (d) 2 00 + 0 + + 9 0 + + 0 + 2 00 = 200 + 0 + + 0.9 + 0 + 0.002 = 2.902 (e) 0 00 + 0 + 2 + 2 0 + 4 + 00 = 0 + 0 + 2 + 0.2 + 0.04 + 0.00 = 2.24 000 000 3. Write the following decimals in the place value table. (a) 0.29 (b) 2.08 (c) 9.60 (d) 48.32 (e) 200.82 Soln.: (a) (b) (c) (d) (e) Numbers 0.29 2.08 9.60 48.32 200.82 Hundreds 00 0 0 0 2 Tens 0 0 0 4 0 Ones 0 2 9 8 0 Tenths 0 2 0 6 3 8 Hundredths 00 9 8 0 2 Thousandths 000 0 0 0 0 2 4. Write each of the following as decimals. 4 (a) 20 + 9 + 0 + 00 (b) 37 + (c) 00 2 6 (d) 23 0 000 7 0 6 4 + + 00 000 + + (e) 700 + 20 + + 9 00 Soln.: (a) 20 + 9 + 0.4 + 0.0 = 29.4 (b) 37 + 0.0 = 37.0 (c) 0.7 + 0.06 + 0.004 = 0.764 (d) 23 + 0.2 + 0.006 = 23.206 (e) 700 + 20 + + 0.09 = 72.09. Write each of the following decimals in words. (a) 0.03 (b).20 (c) 08.6 (d) 0.07 (e) 0.032 (f).008 Soln.: (a) Zero point zero three (b) One point two zero (c) One hundred eight point five six (d) Ten point zero seven (e) Zero point zero three two (f) Five point zero zero eight 6. Between which two numbers in tenths place on the number line does each of the given number lie? (a) 0.06 (b) 0.4 (c) 0.9 (d) 0.66 (e) 0.92 (f) 0.7 Soln.: (a) 0.06 lies between 0 and 0.. (b) 0.4 lies between 0.4 and 0.. (c) 0.9 lies between 0. and 0.2. (d) 0.66 lies between 0.6 and 0.7. (e) 0.92 lies between 0.9 and.0. (f) 0.7 lies between 0. and 0.6. 7. Write as fractions in lowest terms. (a) 0.60 (b) 0.0 (c) 0.7 (d) 0.8 (e) 0.2 (f) 0.2 (g) 0.066 Soln.: (a) 0.60 = 60 3 = (b) 0.0 = = 00 00 20 (c) 0.7 = 7 3 = (d) 0.8 = 8 9 = 00 4 00 0 (e) 0.2 = 2 = (f) 0.2 = 2 = 00 4 000 8 (g) 0.066 = 66 000 33 = 00 Exercise 8.3. Which is greater? (a) 0.3 or 0.4 (b) 0.07 or 0.02 (c) 3 or 0.8 (d) 0. or 0.0 (e).23 or.2 (f) 0.099 or 0.9 DECIMALS
(g). or.0 (h).43 or.490 (i) 3.3 or 3.300 (j).64 or.603 Soln.: Before comparing, we write both terms in like decimals : (a) 0.3 < 0.4 (b) 0.07 > 0.02 (c) 3.0 or 0.8 3.0 > 0.8 (d) 0.0 or 0.0 0.0 > 0.0 (e).23 or.20.23 >.20 (f) 0.099 or 0.90 0.099 < 0.90 (g).0 or.0.0 =.0 (h).43 <.490 (i) 3.300 or 3.300 3.300 = 3.300 (j).640 or.603.640 >.603 2. Make five more examples and find the greater number from them. Soln.: Five examples are : (i).8 or.82 (ii).0009 or.09 (iii) 0.0 or 00. (iv). or.0 (v) 4.23 or 42.3 Before comparing, we write both terms in like decimals (i).80 or.82.82 is greater than.8 (ii).0009 or.0900.09 is greater than.0009 (iii) 0.0 or 00.0 00. is greater than 0.0 (iv).0 or.0. is greater than.0 (v) 4.23 or 42.300 42.3 is greater than 4.23 Exercise 8.4. Express as rupees using decimals. (a) paise (b) 7 paise (c) 20 paise (d) 0 rupees 90 paise (e) 72 paise Soln.: (a) Q paisa = Rs. 00 paise= Rs. = Rs. 00. 00 (b) Q paisa = Rs. 00 7 paise= Rs. 7 = 00 Rs. 07. (c) Q paisa=rs. 00 20 paise= Rs. 20 00 = Rs. 020. (d) Q paisa= Rs. 00 Rs. 0 + 90 paise =Rs. 0 + 90 = Rs. 0.90 00 (e) Q paisa = Rs. 00 72 72 paise=rs. 72 = = Rs. 72. 00 00 2. Express as metres using decimals. (a) cm (b) 6 cm (c) 2 m 4 cm (d) 9 m 7 cm (e) 49 cm Soln.: (a) Q cm= m 00 cm = m = 0. m 00 (b) Q cm= m 00 6 cm = 6m = 0. 06 m 00 (c) Q cm= m 00 2 m4cm= + 2 4 m = 24. m 00 (d) Q cm= m 00 9 m7cm = + 9 7 m = 907. m 00 (e) Q cm= m 00 49 49 cm = 49 m = = 49. m 00 00 3. Express as cm using decimals. (a) mm (b) 60 mm (c) 64 mm (d) 9 cm 8 mm (e) 93 mm Soln.: (a) Q mm= cm 0 mm = cm = 0. cm 0 (b) Q mm= cm 0 60 mm = 60 cm = 60. cm 0 (c) Q mm= cm 0 64 mm = 64 cm = 6. 4 cm 0 (d) Q mm= cm 0 9 cm 8mm= + 9 8 cm = 98. cm 0 (e) Q mm= cm 0 93 mm = 93 cm = 93. cm 0 4. Express as km using decimals. (a) 8 m (b) 88 m (c) 8888 m (d) 70 km m 2 DECIMALS Class 6 Mathematics
Soln.: (a) Q m = km 000 8 m= 8km = 0. 008 km 000 (b) Q m = km 000 88 m= 88 km = 0. 088 km 000 (c) Q m = km 000 8888 m= 8888 km = 8. 888 km 000 (d) Q m = km 000 70km m= 70+ km = 70 00km 000.. Express as kg using decimals. (a) 2 g (b) 00 g (c) 370 g (d) kg 8 g (e) 26 kg 0 g Soln.: (a) Q g = kg 000 2 g= 2kg = 0. 002 kg 000 (b) Q g = kg 000 00 g= 00 kg = 0. kg 000 (c) Q g = kg 000 370 g= 370 kg = 3. 70 kg 000 (d) Q g = kg 000 kg 8g= + 8 kg =. 008 kg 000 (e) Q g = kg 000 26kg 0g = + 26 0 kg = 26 00kg 000. Exercise 8.. Find the sum in each of the following : (a) 0.007 + 8. + 30.08 (b) + 0.632 + 3.8 (c) 27.076 + 0. + 0.004 (d) 2.6 + 9.00 + 3.7 (e) 0.7 + 0.42 + 2 (f) 280.69 + 2.2 + 38 Soln.: (a) 0. 007 8. 00 + 30. 080 38. 87 (b). 000 0. 632 + 3. 800 29. 432 (c) 27. 076 (d) 2. 60 0. 0 9. 00 + 0. 004 + 3. 700 27. 630 38. 3 (e) 0. 70 (f) 280. 69 0. 42 2. 20 + 2. 000 + 38. 00 3. 7 343. 89 2. Rashid spent Rs. 3.7 for Maths book and Rs. 32.60 for Science book. Find the total amount spent by Rashid. Soln.: Money spent for Maths book = Rs. 3.7 Money spent for Science book = Rs. 32.60 Total money spent = Rs. 3.7 + Rs. 32.60 = Rs. 68.3 Therefore, total money spent by Rashid is Rs. 68.3. 3. Radhika s mother gave her Rs. 0.0 and her father gave her Rs..80, find the total amount given to Radhika by the parents. Soln.: Money given by mother = Rs. 0.0 Money given by father = Rs..80 Total money received by Radhika = Rs. 0.0 + Rs..80 = Rs. 26.30 Therefore, total money received by Radhika is Rs. 26.30. 4. Nasreen bought 3 m 20 cm cloth for her shirt and 2 m cm cloth for her trouser. Find the total length of cloth bought by her. Soln.: Cloth bought for shirt = 3 m 20 cm = 3.20 m Cloth bought for trouser = 2 m cm = 2.0 m Total length of cloth bought by Nasreen = 3.20 m + 2.0 m =.2 m Therefore, total length of cloth bought by Nasreen is.2 m.. Naresh walked 2 km 3 m in the morning and km 7 m in the evening. How much distance did he walk in all? Soln.: Distance travelled in the morning = 2 km 3 m = 2.03 km Distance travelled in the evening = km 7 m =.007 km Total distance travelled = (2.03 +.007) km = 3.042 km Therefore, total distance travelled by Naresh is 3.042 km. 6. Sunita travelled km 268 m by bus, 7 km 7 m by car and 00 m on foot in order to reach her school. How far is her school from her residence? DECIMALS 3
Soln.: Distance travelled by bus = km 268 m =.268 km Distance travelled by car = 7 km 7 m = 7.007 km Distance travelled on foot = 00 m = 0.00 km Total distance travelled = (.268 + 7.007 + 0.00) km = 22.77 km Therefore, total distance travelled by Sunita is 22.77 km. 7. Ravi purchased kg 400 g rice, 2 kg 20 g sugar and 0 kg 80g flour. Find the total weight of his purchases. Soln.: Weight of rice = kg 400 g =.400 kg Weight of sugar = 2 kg 20 g = 2.020 kg Weight of flour = 0 kg 80 g = 0.80 kg Total weight = (.400 + 2.020 + 0.80) kg = 8.270 kg Therefore, total weight of Ravi s purchases is 8.270 kg. Exercise 8.6. Subtract : (a) Rs. 8.2 from Rs. 20.7 (b) 202.4 m from 20 m (c) Rs..36 from Rs. 8.40 (d) 2.0 km from.206 km (e) 0.34 kg from 2.07 kg Soln.: (a) 20. 7 8. 2 02. 0 \ Rs. 20.7 Rs. 8.2 = Rs. 2.0 (b) 20. 00 202. 4 47. 46 \ 20 m 202.4 m = 47.46 m (c) 840. 36. 304. \ Rs. 8.40 Rs..36 = Rs. 3.04 (d). 206 2. 0 3. \.206 km 2.0 km = 3. km (e) 2. 07 0. 34. 793 \ 2.07 kg 0.34 kg =.793 kg 2. Find the value of : (a) 9.76 6.28 (b) 2.0.27 (c) 8. 6.79 (d).6 9.847 Soln.: (a) 9. 76 628. 3. 476 (b) 2. 0. 27 0. 78 (c) 8. 0 (d). 600 679. 9. 847. 7. 73 3. Raju bought a book for Rs. 3.6. He gave Rs. 0 to the shopkeeper. How much money did he get back from the shopkeeper? Soln.: Total amount given to shopkeeper = Rs. 0 Cost of book = Rs. 3.6 Amount left = Rs. 0.00 Rs. 3.6 = Rs. 4.3 Therefore, Raju got back Rs. 4.3 from the shopkeeper. 4. Rani had Rs. 8.0. She bought one ice-cream for Rs..7. How much money does she have now? Soln.: Total money = Rs. 8.0 Cost of ice-cream = Rs..7 Amount left = Rs. 8.0 Rs..7 = Rs. 6.7 Therefore, Rani has Rs. 6.7 now.. Tina had 20 m cm long cloth. She cuts 4 m 0 cm length of cloth from this for making a curtain. How much cloth is left with her? Soln.: Total length of cloth = 20 m cm = 20.0 m Length of cloth used = 4 m 0 cm = 4.0 m Remaining cloth = 20.0 m 4.0 m =. m Therefore,. m of cloth is left with Tina. 6. Namita travels 20 km 0 m every day. Out of this she travels 0 km 200 m by bus and the rest by auto. How much distance does she travel by auto? Soln.: Total distance travelled = 20 km 0 m = 20.00 km Distance travelled by bus = 0 km 200 m = 0.200 km Distance travelled by auto = (20.00 0.200) km = 9.80 km Therefore, 9.80 km distance is travelled by auto. 7. Aakash bought vegetables weighing 0 kg. Out of this, 3 kg 00 g is onions, 2 kg 7 g is tomatoes and the rest is potatoes. What is the weight of the potatoes? Soln.: Weight of onions = 3 kg 00 g = 3.00 kg Weight of tomatoes = 2 kg 7 g = 2.07 kg Total weight of onions and tomatoes = (3.00 + 2.07) kg =.7 kg Therefore, weight of potatoes = (0.000.7) kg = 4.42 kg Thus, weight of potatoes is 4.42 kg. 4 DECIMALS Class 6 Mathematics
EXERCISE Multiple Choice Questions Level -. The decimal form of 6708 is. 00 (a) 67.08 (b) 670.8 (c) 6.708 (d) 670 2. The lowest form of 0.4 is. 4 9 (a) (b) 00 20 3 (c) (d) 20 20 3. Two tens and six tenths is expressed in decimals as. (a) 2.6 (b) 2.06 (c) 20.6 (d) 26.0 4. The fraction form of 6.2 is. (a) 62 62 (b) 0 00 (c) 2 2 (d) 4 2. Which model shows 0.04 shaded? (a) (b) 9. 9 Find the value of 0 + 0 + 00 + 000. (a) 0.90 (b) 0.9 (c) 0.09 (d).09 0. In 6.32, the digit 3 is in which place? (a) Tenths (b) Hundredths (c) Hundreds (d) Thousands. How many hundredths are there in 4 tenths? (a) 400 (b) 40 (c) 40 (d) 4 2. Anusha has three pieces of ribbons. One piece is 43.7 m long, another 82.6 m long and the third is 63.2 m long. What is the total length of the three pieces of ribbon? (a) 89.60 m (b) 204.40 m (c) 74.60 m (d) 96.40 m 3. The expanded form of 28.00 is. (a) 20 + 8 + (b) 20 + 8 + 0 000 (c) 20 + 8 + (d) 20 + 8 00 0 + 00 4. Which statement is true? (a).69 <.6 (b) 0.6 > 0.602 (c).2 < 2.2 (d) 2. > 2. (c) (d). 2 expressed as a decimal is. 2 (a).2 (b) 2.4 (c) 2. (d) 2.04 6. Which decimal number is greater than 3 4? (a) 0.8 (b) 0. (c) 0.69 (d) 0.7 6. Express 80 mm in cm as. (a) 0.8 cm (b) 80 cm (c) 800 cm (d) 8 cm 7. The decimal form of 2 is. 4 (a) 62. (b) 0.62 (c) 6.2 (d) 0.2 8. The sum of 609.20 + 6.3 + 42 is. (a) 660. (b) 667. (c) 669. (d) 670. 7. The place value of '7' in 32.07 is. (a) Hundredths (b) Tenths (c) Thousandths (d) Thousands 8. The value of ( + 0. + 0.0 + 0.00) is. (a).00 (b). (c) 0. (d).0 9. A man has a hundred rupee note. He bought vegetables for ` 26.7 and fruits for ` 2.4. How much money he has left? (a) ` 47.80 (b) ` 2.40 (c) ` 73.2 (d) ` 37.80 DECIMALS
20. The largest among 4.32, 4.3, 4.23, and.23 is. (a) 4.32 (b) 4.23 (c) 4.3 (d).23 2. 43.266 24.7 + 34.970 is simplified as. (a) 3.769 (b) 3.679 (c) 73.679 (d) 02.793 22. What is the sum of 6 mm, 60 m and 60 cm? (a) 6600.6 cm (b) 6000.6 cm (c) 6060.6 cm (d) 6666 cm 23. Which is the fraction not equivalent to.670? (a) 67 670 6.7 (b) (c) (d) 6.7 00 000 0 24. Subtracting 8 km 73 m from km 60 m, we get. (a) 7.078 km (b) 0.087 km (c) 23.233 km (d) 7.087 km 2. Which of the following decimal numbers are represented by points K and L on the given number line? 0 K L 2 (a) 0.,. (b).,. (c) 0.2, 0. (d)., 2. Level - 2 26. Which of the following set of decimals are arranged in ascending order? (a) 2.90, 2.09, 2.09, 2.9 (b) 2.90, 2.9, 2.09, 2.09 (c) 2.09, 2.09, 2.9, 2.90 (d) 2.9, 2.09, 2.09, 2.90 27. Pushkar purchased a chocolate for ` 2.0, a pastry for `.7 and a packet of chips for ` 8.38. How much money did he spend in all? (a) ` 27. (b) ` 26.63 (c) ` 28.63 (d) ` 20 28. Select the correct match of shaded portion. (a) = 0.3 (b) = 0.6 (c) = 0. (d) = 0. 29. Find the value of (i) 7.432 2.876 + 82.49.90 (ii) 39.286 + 23.43 82.432 + 90.62 (iii) 69.387 37.483 28. + 38.7 (i) (ii) (iii) (a) 42.64 80.9 42.39 (b) 3.4 80.9 3.432 (c) 42.64 70.946 3.432 (d) 3.4 70.946 42.39 30. The corner store sells 29.9 litres of milk on Thursday and.32 litres more than this quantity on Friday. The following day, 8.94 litres less milk were sold than on Friday. How many litres of milk did they sell on Saturday? (a) 60.7 litres (b) 37.3 litres (c) 22.29 litres (d) 99.6 litres Fill in the Blanks. 0. can be written in words as. 2. 6.8 + 4.83 0.94 =. 3. A bag contains 7.0 kg of rice, another bag contains.7 kg of rice. The total weight of the rice is kg. 4. The difference of place values of 3 in 32.3 is.. Difference of 30 and.4 is. 6. Express m in cm as. 7. 4.904 = 0 + 4 + 9 + 4 8. is than 0.0. 2 9. separates whole number and fractional part of a decimal number. 0. 6.42 and 8.4 are decimals. True or False. 2.0 and 2.00 are not equivalent decimals. 2. The expanded form of 2.06 is (2 ) + 6 00. 3. The place value of 9 in the decimal 627.98 is thousandths. 4. 2 8 is expressed in decimal as 2.08. 0. The weight of an empty gas cylinder is 8 kg 7 g. The weight of the gas contained in it is 2 kg 6 DECIMALS Class 6 Mathematics
30 g. The total weight of the cylinder filled with gas is 30 kg 420 g. 6. Decimals cannot be represented on the number line. 7. Numbers written in the decimal form are called whole numbers. 8. The decimal form of 2 is 0.06. 4 9. The shaded part of shows 0.7. 0..23 is greater than.02. Match the Following In this section, each question has two matching lists. Choices for the correct combination of elements from List-I and List-II are given as options (a), (b), (c) and (d) out of which one is correct.. Match the following. List-I List-II (P) 2.220. 2 + 2 00 (Q) 2.022 2. 2 + 2 0 + 2 00 (R) 2.020 3. 20 + 2 0 + 2 000 (S) 20.202 4. 2 + 2 00 + 2 000 Code: P Q R S (a) 4 2 3 (b) 4 2 3 (c) 2 4 3 (d) 2 4 3 2. Match the following. List-I (P) 2 (Q) 3 4 (R) 7 0 (S) 4 List-II. 0.70 2. 0.2 3. 0.40 4. 0.7 Code: P Q R S (a) 4 3 2 (b) 3 4 2 (c) 2 3 4 (d) 3 4 2 3. Match the following. List-I List-II (P) The snowfall during three. 7.09 winter months was 30. cm, 4.2 cm, and 2.2 cm. Then the total snowfall in these three months is (in cm) (Q) Kritika's weight is 3 kg 7 gm and her sister Khushi's weight is 27 kg 980 gm. Kritika is heavier by (in kg)? 2. 2.7 (R) Naresh drive 42 km 3 m in 3. 0 the morning and 2 km 7 m in the evening. The distance he drive in all (in km) is (S) Anu has ` 28.0. She bought 4. 67.042 some ice-creams for ` 20.7. The money she have now (in `) is Code: P Q R S (a) 3 2 4 (b) 3 2 4 (c) 3 4 2 (d) 3 4 2 Assertion & Reason Type Directions: In each of the following questions, a statement of Assertion (A) is given followed by a corresponding statement of Reason (R) just below it. Of the statement, mark the correct answer as (a) If both assertion and reason are true and reason is the correct explanation of assertion. (b) If both assertion and reason are true but reason is not the correct explanation of assertion. (c) If assertion is true but reason is false. (d) If assertion is false but reason is true.. Assertion : 0.7, 0.70, 0.700 are the equivalent decimals. Reason : Number of zero at the end of decimal number change the value of the number. 2. Assertion : The fraction form of 6.2 is 62 00. Reason : In the denominator, write followed by as many zeroes as there are decimal place in the given decimal. DECIMALS 7
3. Assertion : The number 2.902 is expressed in expanded form as 2 00 0 + 9 0 2 00. Reason : As we go from left to right, the multiplying factor becomes 0 of the previous factor. 4. Assertion : The sum of 27.8, 7.09 and 68.7 is 888.9 Reason : To subtract decimal numbers column wise, we place them correctly in the place value table and subtract them in the same way as of whole numbers.. Assertion : Expressing 73 m into km is 73000 km. Reason : m = 000 km Comprehension Type PASSAGE : To change a decimal numeral to a common fraction, express the decimal as a fraction with denominator 0, 00, 000 and then reduce it to its lowest term.. The sum of 67.2,., 9.8 in fraction form is (a) 826 826 (b) 00 0 (c) 826 (d) 820 00 2. Amit bought a comic book for ` 4.60 and a magazine for ` 70.00. What is the total amount spent by Amit (Express in lowest fractional form). (a) 02 (c) 78 (b) (d) 6 2 6 3. Convert 9.07 kg in grams. (a) 9070 g (b) 907 0 g (c) 907 g (d) None of these PASSAGE 2 : A squash ball weighs 3400 mg, a cricket ball weighs 4 g, a basketball weighs 0.6 kg and a football weighs 3 kg.. Which sports ball is lighter in weight? (a) Cricket ball (b) Football (c) Squash ball (d) Basketball 2. What is the weight (in kg) of basketball and football? (a) 0.36 kg (b) 3.6 kg (c) 36 kg (d) 3 kg 3. What is the total weight of all the balls in mg? (a) 3729 mg (b) 3.729 mg (c) 3729000 mg (d) 0.3729 mg Subjective Problems Very Short Answer Type. Write in decimal form. 000 2. 0.23 or 0.2, which is greater? 3. What is the sum of 2.7, 7.83 and 6.2? 4. Express 46 rupees 87 paise as rupees using decimals.. Subtract 0.2 from 0.37. 6. Express 6 0 + 8 as a decimal. 00 7. Simplify : 6 0.4 0.87. 8. Write 3 as a decimal. 9. Show.8 on the number line. 0. Write in order from least to the greatest: 2., 2.0, 2.0. Short Answer Type. Write the following numbers in the place value table and write their number names. (a) 8. (b) 2.3 2. Arrange the following decimals in descending order: 8.88, 8.088, 88.8, 88.08, 8.008 3. Write the following decimals in expanded form. (a) 42.607 (b) 243.26 4. Find the sum of 40 rupees 80 paise and 9 rupees 0 paise.. Ramesh and Rahul walked back to their homes by walking 3.2 km and 3.8 km respectively. Who walked more distance and by how much? 6. Simplify: 3.23 + 29.37 + 8.206 + 0.3376 7. A man purchases an almirah for ` 367, gives ` 72.0 as its cartage and spends ` 64.80 on its repair. How much does the almirah cost him? 8 DECIMALS Class 6 Mathematics
8. The height of Jyoti and Geetanjali is.9 m and 0.94 m, respectively. How much shorter is Geetanjali than Jyoti? 9. Simplify: 3. 34.68 + 64.7 28.9. 0. From a ribbon of length m, two pieces of 7 m and 6. m were cut. Find the remaining part of length. Long Answer Type. Rahim, Ravinder and Rohit bought 8. litres, 7.2 litres and 9.4 litres milk respectively from a milk booth. How much milk did they buy in all? If there was 30 litres of milk in booth, find the quantity of milk left. 2. Simplify: (i) (8.6 4.43) (03.37 + 23) (ii) 9.469 + 39.6 7.2 + 4.0 (iii) 23.667 2. 9.20 + 80.432 3. Rajendra purchased 6 kg 2 g of fruits and 4 kg 3 g of vegetables and put them in a bag. If this bag with these contents weighs kg, find the weight of the empty bag. 4. The distance between Raj's house and his office is 6 km. He covers km 3 m by car, 3 km 7 m by bus and the rest on foot. How much distance does he cover by walking?. How many numbers with 2 decimal places between 2. and 3 contain the digit 7. What is the difference of first seven numbers from last seven numbers? Integer Type Questions In this section, each question, when worked out will result in one integer from 0 to 9 (both inclusive).. What is the decimal part of the sum if we add 8.3 and.6? 2. What is the hundredth part of the decimal number.04? 3. What is the sum of the digits of the product of the sum and the difference of 4. and 2.? 4. How many zeroes followed by if we express 8 gm into kg?. What is the whole number part in sum of 3 + 0.4 + 0.0 + 0.00? 6. The height of Sonu is.2 m and that of Reena is.3 m. How much is Reena taller than Sonu (in cm)? 7. Subtract 2. from 8., what will we get? 8. Write the numerator of decimal form 0.0 expressed in fractional form? 9. What is the tenth place value if we add 3. and.7? 0. What is the value of P for 0.04 = P 2? DECIMALS 9
Decimals CHAPTER 8 Multiple Choice Questions. (a) : Decimal form of 6708 00 = 67.08 2. (b): 0.4 = 4 00 = 9 20 3. (c) : Two tens and six tenths = 2 0 + 6 0 = 20.6. 4. (b): 6.2 = 6.2 00 00 = 62 00. (d): (a) 60 parts are shaded out of 00 parts i.e., 60 00 = 0.6 (b) 40 parts are shaded out of 00 parts i.e., 40 00 = 0.4 (c) 4 parts are shaded out of 00 parts i.e., 4 00 = 0.4 (d) 4 parts are shaded out of 00 parts 4 i.e., 00 = 0.04 6. (d): As mm = 0 cm 80 mm = 80 0 = 8 cm 7. (c) : 2 4 8. (b): 609. 20 6. 30 + 42. 00 667. 0 = 2 2 4 2 = 62 00 = 6.2 9. (c) : We have 0 tens, 9 hundredths and thousandths = 0.09 0. (b): The expanded form of 6.32 is 0 + 6 + 0 + 3 00 + 2 000 Here, 3 is in the hundredth place.. (b) : As tenths = 0 hundredths 4 tenths = 40 hundredths 2. (a) : Length of first piece of ribbon = 43.7 m Length of second piece of ribbon = 82.6 m Length of third piece of ribbon = 63.2 m Total length of three pieces of ribbon = (43.7 + 82.6 + 63.2) m = 89.6 m 3. (b): 28.00 = 2 0 + 8 + = 20 + 8 + 000 4. (b): (a) We have,.69 <.6 000 but.69 >.60 (as hundredths part, 9 > 0), So, (a) is incorrect. (b) We have, 0.60 > 0.602. So, (b) is correct. (c) We have,.2 < 2.2 but.2 > 2.2 (as whole part, > 2) So, (c) is incorrect. (d) We have, 2. > 2. but 2. > 2.0 (as thousandths part, > 0) So, (d) is incorrect.. (d): 2 2 = 2 + 2 To make the denominator 00, multiply 2 by 4 2 + 2 = 2 + 4 2 4 = 2 00 00 + 4 00 = 200 + 4 00 = 204 00 = 2.04 6. (a) : As 3 4 = 3 2 4 2 = 7 00 = 0.7 [To make the denominator 00, multiply by 2] 0.8 is greater than 0.7. DECIMALS M33
7. (c) : 32.07 = 3 0 + 2 + 0 + 7 000 = 30 + 2 + 0 + 7 000 Place value of 7 in 32.07 is thousandths. 8. (b): Converting all decimal numbers into like decimals.000 + 0.00 + 0.00 + 0.00 =. 9. (a) : Money spent on vegetables = ` 26.7 Money spent on fruits = ` 2.4 Total money = ` 00 Money left = ` 00 ` (26.7 + 2.4) = ` 00 ` 2.20 = ` 47.80 20. (c) : Clearly, 4.3 > 4.32 > 4.23 >.23 The largest decimal number is 4.3. 2. (b): 43.266 + 34.970 24.7 = 3.679 4 3. 2 66 7 8. 2 36 + 3 4. 9 70 2 4. 7 7 8. 2 36 3. 6 79 22. (c) : Converting the given quantities into cm As mm = 0 cm 6 mm = 6 cm = 0.6 cm 0 and m = 00 cm 60 m = 6000 cm 6 mm + 60 m + 60 cm = 0.6 cm + 6000 cm + 60 cm = 6,060.6 cm 23. (d): We have,.670 = 670 000 = 67 00 = 6.7 0 6.7 is not equivalent to.670. 24. (d): Converting the given quantities into km As m = 000 km 73 m = 73 km = 0.073 km 000 8 km 73 m = 8 km + 0.073 km = 8.073 km Also, km 60 m = km + 60 000 km = km + 0.60 km =.60 km Their difference = (.60 8.073) km = 7.087 km 2. (a) : Point K represents 0. and point L represents.. 26. (c) : We have, 2.90, 2.09, 2.09, 2.9 As whole part of all the decimal numbers is same i.e., 2. M34 DECIMALS Come to the tenths place, 2.09 is the smallest and 2.90 is the largest. In 2.09 and 2.9, digits at hundredths place are 0 and respectively. 2.09 < 2.09 < 2.9 < 2.90 (c) is in ascending order. 27. (b): Cost of a chocolate = ` 2.0 Cost of a pastry = `.7 Cost of a packet of chips = ` 8.38 Add all the costs. ` 2. 0 `. 7 + ` 8. 3 8 ` 2 6. 6 3 Therefore, Pushkar spent ` 26.63 in all. 28. (d): (a) 2 = 0.2 0.3 0 (b) 7 = 0.7 0.6 0 4 (c) = 0.4 0. 0 (d) 0 = 0. 29. (d) : (i) 7.432 2.876 + 82.49.90 = 4.6 + 30.8 = 3.4 (ii) 39.286 + 23.43 + 90.62 82.432 = 3.3866 82.432 = 70.946 (iii) 69.387 37.483 + 38.7 28. = 3.904 + 0.23 = 42.39 30. (c) : Milk sold on Thursday = 29.9 litres 2 9. 9 litres +. 3 2 litres 4. 2 3 litres Milk sold on Friday = 4.23 litres Now, 4. 2 3 litres 8. 9 4 litres 2 2. 2 9 litres Milk sold on Saturday = 22.29 litres Fill in the Blanks. Zero point one five 2. 0.69; 6.8 + 4.83 0.94 = 2.63 0.94 = 0.69 3. 9.2; Total weight of rice = 7.0 kg +.7 kg = 9.2 kg 4. 29.97; Required difference = 3 0 3 = 30 0.03 = 29.97 00. 4.; 30.00.4 = 4. Class 6 Mathematics
6. 00 cm; m= ( 00) cm = 00 cm 7. 0, 000; 0 + 4 + 9 + 4 0 000 8. Greater; 2 = 2 = = 0. is greater than 0.0. 0 9. Decimal point 0. Like True or False. False : 2.0 and 2.00 are equivalent decimals. 2. True 3. False : The place value of 9 in 627.98 is 9 00 (hundredth) 4. False : 2 8 0 = 2 + 8 = 2 + 0.8 = 2.8 0. False : Total weight of cylinder filled with gas = 8 kg 7 g + 2 kg 30 g = 8 kg + 7 30 kg + 2 kg + 000 000 kg = 8 kg + 0.07 kg + 2 kg + 0.30 kg = 8.07 kg + 2.30 kg = 30.42 kg = 30 kg 42 g 6. False : Decimals can be represented on the number line. 7. False : Numbers written in the decimal form are called decimal numbers. 8. False : 2 4 = 2 2 4 2 = 0 00 = 0. 9. True 0. True Match the Following. (d): P 2; Q 4; R ; S 3 (P) 2.220 = 2 + 2 0 + 2 00 = 2 + 2 0 + 2 00 (Q) 2.022 = 2 + 2 00 + 2 000 = 2 + 2 00 + 2 000 (R) 2.020 = 2 + 2 00 = 2 + 2 00 (S) 20.202 = 2 0 + 2 0 + 2 000 = 20 + 2 0 + 2 000 2. (b): P 3; Q 4; R ; S 2 (P) 2 = 2 2 2 = 4 = 0.4 = 0.40 0 [To make denominator 0, multiply by 2] (Q) 3 4 = 3 2 4 2 = 7 00 = 0.7 (R) 7 = 0.7 = 0.70 0 (S) 4 = 2 4 2 = 2 00 = 0.2 3. (c) : P 3; Q ; R 4; S 2 (P) Total snowfall in three months = (30. + 4.2 + 2.2) cm = 0 cm (Q) Kritika's weight = 3 kg 7 gm = 3 kg + 7 kg = 3 kg + 0.07 kg = 3.07 kg 000 Khushi's weight = 27 kg 980 gm = 27 kg + 980 kg = 27 + 0.980 kg = 27.980 kg 000 Required difference = 3.07 kg 27.980 kg = 7.09 kg Kritika is heavier by 7.09 kg. (R) Naresh drive in morning = 42 km 3 m = 42 km + 3 km = 42 km + 0.03 km 000 = 42.03 km Naresh drive in evening = 2 km 7 m 7 = 2 km + km = 2 km + 0.007 km 000 = 2.007 km Total distance Naresh drive in all = 42.03 km + 2.007 km = 67.042 km (S) Total money Anu had = ` 28.0 Money spent on ice-cream = ` 20.7 Money left with Anu = ` 28.0 ` 20.7 = ` 2.7 Assertion & Reason Type. (c) : Addition of zero at the end of decimal number does not change the value of the number. Assertion : True; Reason : False DECIMALS M3
2. (a) : Assertion : True; Reason : True and Reason is the correct explanation of Assertion. 3. (d): As, 2.902 = 2 00 + 0 + + 9 0 + 2 000 Assertion : False; Reason : True 4. (b) : As 27.80 + 7.09 + 68.70 = 888.9 To add decimal numbers column wise, we place decimal numbers and decimal points correctly one below the other and add them as in case of whole numbers. Assertion : True; Reason : True but Reason is not the correct explanation of Assertion.. (d) : As 73 m = 0.73 km Assertion : False; Reason : True Comprehension Type PASSAGE. (b): As 67.2 +. + 9.8 = 67.2 +.0 + 9.8 = 82.6 In fraction form, 82.6 = 826 0 2. (c) : ` 4. 60 + ` 7 0. 00 `. 60 Total amount spent by Amit = `.60 Fractional form of.60 = 60 00 = 6 0 In lowest form, 6 2 0 2 = 78 3. (a) : We have, 9.07 kg = 907 00 kg As kg = 000 g 9.07 kg = 907 000 g = 9070 g 00 PASSAGE 2. (c) : Converting all quantities into g. Weight of a squash ball = 34000 mg Weight of a squash ball in grams = 34000 000 g = 34 g Weight of a cricket ball = 4 g Weight of a basketball = 0.6 000 g = 60 g Weight of a football = 3 000 g = 3000 g \ 34 < 4 < 60 < 3000 \ The weight of squash ball is the lightest. 2. (b) : Total weight of a basketball and football = 0.6 + 3.00 = 3.6 kg 3. (c) : Total weight of balls = 34 + 4 + 60 + 3000 g = 3729 g In mg, 3729 000 = 3729000 mg Subjective Problems Very Short Answer Type. The decimal form of 000 = 0.00 2. Upto hundredth place, numbers are same At thousandths place > 3 \ 0.2 > 0.23 3. 2. 7 7. 8 3 + 6. 2 0 3 6. 2 0 Required sum = 36.20 4. 46 rupees 87 paise = 46 + 87 00 Q paise = 00 rupees = 46 + 0.87 = 46.87 rupees. 0. 3 7 0. 2 0. 2 6. 6 0 + 8 00 = 6 0 + 8 00 = 0.68 7. Converting 6, 0.4, 0.87 into equivalent decimals. 6.00 0.40 0.87 = 6.00.27 = 4.73 8. 3 = 3 + = 3 + 2 0 = 3 0 + 2 0 0 = 30 + 2 = 32 0 0 = 3.2 9. As <.8 < 2, divide the unit distance from and 2 into 0 equal parts and take 8 parts in the number line. P P represents.8. 0. As, 2. = 2 + 0 + 0 + 0 2.0 = 2 + 0 + 000 2.0 = 2 + 00 + 000 Clearly, 2.0 < 2.00 < 2.0.8 2 M36 DECIMALS Class 6 Mathematics
. S. no. Number Short Answer Type Hundreds Tens Ones Tenths Hundredths (a) 8. 0 8 0 (b) 2.3 2 3 (a) 8. Eighteen and five tenths (b)2.3 One hundred twenty five and thirty one hundredth 2. We have, 8.88, 8.088, 88.8, 88.08, 8.008 Converting into equivalent decimals, we get 8.880, 8.088, 88.800, 88.080, 8.008 In decending order, 88.800, 88.080, 8.880, 8.088, 8.008. 3. (a) 42.607 = 4 00 + 0 + 2 + 6 0 + 7 000 = 400 + 0 + 2 + 6 0 + 7 000 (b) 243.26 = 000 + 2 00 + 4 0 + 3 + 2 0 + 6 00 = 000 + 200 + 40 + 3 + 2 0 + 6 00 4. 40 rupees 80 paise in rupees = 40 + 80 rupees = 40 + 0.80 = 40.80 rupees 00 9 rupees 0 paise = 9 + 0 rupees = 9 + 0.0 = 9.0 rupees 00 Sum of 40 rupees 80 paise and 9 rupees 0 paise 4 0. 8 0 rupees + 9. 0 rupees 3 6. 3 0 rupees. Rahul walked 3.8 km. Ramesh walked 3.2 km = 3.20 km Now, in tenth place > 2 So, 3.8 km > 3.20 km \ Rahul walked more distance than Ramesh As, 3.8 3.20 = 0.38 km \ Rahul walked more distance by 0.38 km. 6. Convert 3.23, 29.37, 8.206, 0.3376 into like decimals. So, 3.2300, 29.370, 8.206, 0.3376 3. 2 3 0 0 2 9. 3 7 0 8. 2 0 6 + 0. 3 3 7 6 4. 4 4 2 Required sum = 4.442 7. Cost of almirah = ` 367 Cost for its cartage = ` 72.0 Cost on its repair = ` 64.80 Total money spent for almirah = ` (367 + 72.0 + 64.80) = ` 392.30 8. Height of Jyoti =.9 m Height of Geetanjali = 0.94 m Subtract Geetanjali's height from Jyoti's height.. 9 0. 9 4 0. 6 Geetanjali is 0.6 m shorter than Jyoti. 9. 3.0 34.68 + 64.7 28.90 [Converting into like decimals] = 8.82 + 3.8 = 4.67 0. Original length of ribbon = m Length of ribbon cut out = 7 m + 6. m = 3. m Remaining part of length = m 3. m =. m Long Answer Type. Milk bought by Rahim = 8. litres Milk bought by Ravinder = 7.2 litres Milk bought by Rohit = 9.4 litres Milk bought by all = (8. + 7.2 + 9.4) litres = 2. litres Quantity of milk left in booth = 30 litres 2. litres = 4.8 litres 2. (i) Consider, 8.6 4.43 Put zeroes in 8.6 to make four decimal places i.e. 8.600 So, 8.600 4.43 = 40.96...() Now consider, 03.37 + 23 Put zeroes in 23 to make two decimal places So, 03.37 + 23.00 = 76.37...(2) Subtract (2) from (), we get 40.96 76.3700 = 76.73 (ii) Consider 9.469 + 39.6 Put zeroes in 39.6 to make three decimal places i.e., 39.60 DECIMALS M37
So, 9.469 + 39.60 = 3.9...() Now consider, 7.2 + 4.0 Put zeroes in 4.0 to make three decimal places i.e., 4.00 So, 7.2 + 4.00 = 42.7...(2) Adding () and (2), we get 3.9 42.7 = 88.364 (iii) Consider 23.667 2. Put zeroes in 2. to make three decimal places i.e., 2.0 So, 23.667 2.0 = 2.7...() Now consider, 9.20 + 80.432 = 6.227...(2) Adding () and (2), we get 2.7 + 6.227 = 82.344 3. Weight of fruits = 6 kg 2 g = 6 kg + 2 kg = 6 kg + 0.02 kg = 6.02 kg 000 Weight of vegetables = 4 kg 3 g = 4 kg + 3 kg = 4 kg + 0.3 kg = 4.3 kg 000 Weight of fruits and vegetables = 6.02 kg + 4.3 kg = 0.38 kg Weight of bag with contents = kg \ Weight of empty bag = kg 0.38 kg = 0.62 kg 4. Distance convered by car = km 3 m 3 = km + km = km + 0.03 km =.03 km 000 Distance covered by bus = 3 km 7 m 7 = 3 km + km = 3 km + 0.07 km = 3.07 km 000 Total distance covered by car & bus = (.03 + 3.07) km = 4. km Distance between Raj's house and his office = 6 km Distance covered by walking = 6 km 4. km =.89 km. Between 2. and 3, there are 4 numbers with 2 decimal places contain the digit 7 i.e., 2.7, 2.67, 2.70, 2.7, 2.72, 2.73, 2.74, 2.7, 2.76, 2.77, 2.78, 2.79, 2.87, 2.97 Consider first seven numbers, 2.7 + 2.67 + 2.70 + 2.7 + 2.72 + 2.73 + 2.74 = 8.84 Now consider last seven numbers = 2.7 + 2.76 + 2.77 + 2.78 + 2.79 + 2.87 + 2.97 = 9.69 Now, their difference = 9.69 8.84 = 0.8 Integer Type Questions. (9) : Adding 8.3 and.6, we get 8.3 +.6 = 3.9 The decimal part is 9. 2. (4) : In.04, 4 is the hundredth part. 3. () : Sum of 4. and 2. = 7 Difference of 4. and 2. = 2 Product = 7 2 = 4 Sum of the digits of 4 = + 4 = 4. (3) : gm = 000 kg 8 8 gm = 000 kg. (3) : 3 + 0.4 + 0.0 + 0.00 Put zeroes in 3, 0.4, 0.0 to make three decimal places i.e., 3.000, 0.400, 0.00 3.000 + 0.400 + 0.00 + 0.00 = 3.4 The whole number part in 3.4 is 3. 6. () : Height of Sonu =.2 m Height of Reena =.3 m Reena is (.3.2) m = 0.0 m = 0.0 00 = cm taller than Sonu. 7. (6) : 8. 2. = 6.0 8. () : 0.0 = 00 \ Numerator is. 9. (0) : 3. +.7 = 3.0 +.7 =.07 So, the tenths place value is 0. 0. () : 0.04 = P 2 4 00 = P 2 4 4 00 4 = P 2 2 = P 2 P = M38 DECIMALS Class 6 Mathematics