Lesson 4: Place Value of Decimal Numbers

Transcription

1 Lesson 4: Place Value of Decimal Numbers Prayer Is the Key: For the Lord gives wisdom, and from His mouth come knowledge and understanding. Proverbs 2:6(NIV) Almighty God, grant unto me wisdom, knowledge and understanding to deal with this situation before me (state the situation), in Jesus name I ask with thanksgiving. Amen. Specific Objective At the end of the lesson the student should be able to: (a) define a decimal fraction; (b) identify the place value of digits of decimal numbers; (c) write a decimal number in expanded notation; (d) solve problems involving place values. 4.0 Quick Review of Last Lesson: Place Value in Base 2 Question ( 3 marks) (a) What is the place value of the digit "0" in the number ? (b) Convert from base 2 to base 10. (c) Covert 27 from base 10 to base 2 (Answers at the end of this lesson) 4.1 What Is A Decimal Fraction? (a) A decimal fraction is any number less than one and written as a decimal. (b) Examples of decimal fractions are 0.675, 0.02, and (c) The 0 before the point in each decimal fraction shows that the number is less than 1, and it is not significant (in other words, it can be omitted and the value of the numbers do not change). Therefore, is the same as.675 and 0.02 is the same as.02.

2 4.2 Meaning of the Decimal Point Consider the number We know that represents the whole number part of the number , while the.539 represents the decimal part of the number. Therefore, the decimal point (.) shows where the whole number,2 476, ends and the decimal fraction,.539, begins. Example 1: What is the place value of : (a) 5 in ? (b) 7 in ? (c) 3 in ? (d) 4 in ? (e) 9 in ? (f) 2 in ? (g) 6 in ? To answer this question, consider Table 2 below. The table shows the place values for the digits in thousands hundreds tens units decimal point tenths hundredths tens of hundreds of Table 2 (a) The 5 is located in the tenths place. Therefore the place value of 5 is 5 tenths or 5/10 or 0.5 (b) The 7 is located in the tens position. Therefore the place value of 7 is 7 tens or 70. (c) The 3 is located in the hundredths position. Therefore the place value of 3 is 3 hundredths or 3/100 or (use your calculator to check that 3/100 = 0.03.) (d) The 4 is located in the hundreds position. Therefore, the place value of 4 is 4 hundreds or 400. (e) The 9 is located in the position. Therefore the place value of the 9 is 9/1000 or Self-Assessment 4A 1. Write down the place value of: (a) 2 in 6.32 (b) 8 in (c) 9 in (d) 7 in (e) 4 in (f) 0 in ( 6 marks)

3 2. Calculate, using your calculator, the (a) SUM and (b) POSITIVE DIFFERENCE of the place values of the 3 and 5 in the number ( 2 marks) 3. Which of the following is not a decimal fraction? (a) 0.23 (b) (c) (d) (e) (f) ( 6 marks) 4. Match correctly the numbers in column A with statements in column B. ( 6 marks) Column A Column B The place value of 3 is The place value of 4 is The place value of 3 is The place value of 4 is The place value of 3 is The place value of 4 is Write down the place value for each of the digits shown in red in Table 3 below. For example, in (a) The place value of 6 is 6 tenths or 6/10 or 0.6. Question 5 thousands hundreds tens units decimal point tenths (a) (b) hundredths (c) (d) tens of (e) (f) hundreds of See s to Self-Assessment 4A Table 3 ( 11 marks) 4.4 Writing Decimal Fractions in Expanded Notation Recall (see Lesson 2)the different ways in which the numbers 1, 10, 100, 1000, , and can be written: Ones (unit): 1 = 10 0 Ten: 10 = 10 1 Hundred: 100 = 10 x 10 = 10 2 Thousand: 1000 = 10 x 10 x 10 = 10 3 Ten thousand: = 10 x 10 x 10 x 10 = 10 4 Hundred Thousands: = 10 x 10 x 10 x 10 x 10 = 10 5 Million: = 10 x 10 x 10 x 10 x 10 x 10 = 10 6

4 Consider Table 4 below: Hundreds Thousands 1000 or or 10 2 Tens 10 or 10 1 Units decimal 1 or 10 0 point Tenths 1/10 or 10-1 Hundredths 1/100 or 10-2 Thousandths 1/1000 or 10-3 Tens of 1/ or 10-4 Hundreds of 1/ or 10-5 Table 4 From Table 4 above we observe the following pattern: Thousands: 1000 = 10 3 Hundreds: 100 = 10 2 Tens: 10 = 10 1 Units (ones) : 1 = 10 0 Tenths: 1/10 = 10-1 Hundredths: 1/100 = 10-2 Thousandths: 1/1000 = 10-3 Tens of : 1/ = 10-4 Hundreds of Thousandths: 1/ = 10-5 Can you complete the next column for millionths (not shown on table) following the pattern above? Millionths : 1/ =? If you say Millionths = 1/ = 10-6 then you are correct. Well done! Example 2: Write the following in expanded notation: (a) (b) (c) You can draw up a similar table as shown in Table 5, from which you can easily write your answers: Hundreds Thousands 1000 or or 10 2 Tens 10 or 10 1 Units decimal 1 or 10 0 point Tenths 1/10 or 10-1 Hundredths 1/100 or Thousandths 1/1000 or 10-3 Tens of 1/ or Hundreds of 1/ or 10-5 (a) = (3 x 10 3 ) + (7x10 2 ) + (5x10 1 ) + (2 x 10 0 ) + (9x10-1 ) +(4x10-2 ) + (6x10-3 ). (b) = (1 x 10 1 ) + (7x10-1 ) +(6x10-2 ) + (2x10-3 ) + (9x10-4 ) + ( 3 x10-5 ). (c) = (4x10 2 ) + (2x10 1 ) + (9 x 10 0 )) +(2x10-2 ) + (8x10-3 ) + (7x10-4 ) + ( 5 x10-5 ). Note in (b) 0 x 10 1 =0, and in (c) 0 x 10-1 = 0. Therefore, both expressions are omitted.

5 Example 3: Write the following expanded notations as ordinary numbers: (a) (7 x 10 3 ) + (4x10 2 ) + (2x10 1 ) + (6 x 10 0 ) + (8x10-1 ) +(5x10-2 ) + (3x10-3 ). (b) (5 x 10 2 ) + (8x10 1 ) + (2 x 10 0 ) + (3x10-1 ) +(7x10-2 ) + (1x10-3 ) + (6x10-4 ). (c) (6x10 1 ) + (9 x 10 0 )) + (4x10-1 ) + (6x10-2 ) + (3x10-3 ) + (2x10-4 ) + ( 7 x10-5 ). (a) (7 x 10 3 ) + (4x10 2 ) + (2x10 1 ) + (6 x 10 0 ) + (8x10-1 ) +(5x10-2 ) + (3x10-3 ) = (7x1000) + (4 x 100) + (2 x 10) + (6x1) + (8/10) + (5/100) + (3/1000) = = Note: You can use your calculator to check your working for 8/10, 5/100 and 3/1000 and then to find the total, as shown. (b) (5 x 10 2 ) + (8x10 1 ) + (2 x 10 0 ) + (3x10-1 ) +(7x10-2 ) + (1x10-3 ) + (6x10-4 ) = (5 x 100) + (8 x 10) + (2x1) + (3/10) + (7/100) + (1/1000) + (6/10 000) = (c) (6x10 1 ) + (9 x 10 0 )) + (4x10-1 ) + (6x10-2 ) + (3x10-3 ) + (2x10-4 ) + ( 7 x10-5 ) + ( 8 x10-6 ) = (6 x 10) + (9 x 1) + (4/10) + (6/100) + (3/1000) + (2/10 000) + 7/ / = = Answers to Quick Review (a) 16 (b) 111 (c) Self-Assessment # 4B 1. Write the following in expanded notation: (a) (b) (c) (d) ( 4 marks) 2. Write the following expanded notations as ordinary numbers: (a) (8 x 10 3 ) + (6x10 2 ) + (3x10 1 ) + (4 x 10 0 ) + (7x10-1 ) +(2x10-2 ) + (9x10-3 ). (b) (4 x 10 2 ) + (7x10 1 ) + (5 x 10 0 ) + (6x10-1 ) +(3x10-2 ) + (7x10-3 ) + (8x10-4 ). (c) (9x10 2 ) + (4x10 1 ) + (7 x 10 0 )) + (8x10-1 ) + (5x10-2 ) + (6x10-3 ) + (2x10-4 ) + ( 4 x10-5 ). See s to Self-Assessment 4B ( 3 marks) 4.7 Interactive Assessment Go to Interactive Assessment #4 Return to Courses Posted by Alton: Wed. 31 st Aug. 2011