6 Number System 6. Decimals. Write each of the following as a decimal. 7 0 7 00 0 (d) 0 000 (e) 00 (f) 000 (g) 3 00 (h) 999 000. Write each of the following as a fraction. 0.6 0.37 0.07 (d) 0.9 (e) 0.00 (f) 0.999 (g) 0.093 (h) 0. 3. Read the value indicated by each pointer 6 7 0 (d) 0. 0.6 3. 3.3 (e) (f) 0. 0.6.7.8. Copy each scale three times and indicate with a pointer each of the numbers given...6 0.7 0.8. Calculate (i). (i) 0.7 (ii).7 (ii) 0.79 (iii). (iii) 0.70. 3. 6. + 7. 7. + 97. (d). 3 + 3. (e) 6. +. 6 (f) 39. 8 + 38. 9 (g) 7. 3 + 6. + 0. 3 (h). 3. (i) 6.. (j) 9. 7. (k) 83.. (l). 6. (m) 7. 7. (n) 86. 37. (o) 73.. 6 (p). + 3. (q) 36. + 7. (r) 37. + 7. (s). + 37. 3 (t) 7. 6 + 9. 8 68
6. Convert the following amounts in pence to s. (i) 7 p (ii) p (iii) 700 p (iv) 763 p Convert the following amounts in s to pence. (i).99 (ii) 0.07 (iii) (iv) 3.7 7. Find a decimal number between. and.6 0.9 and 0.0. and.3 (d) 7.37 and 7.38 8. Put these decimal numbers in ascending order..7,.,.7,.7,.,.77 9. Felix has 8. m of model railway track and Gerry has 6.6 m. What is the total length of their track? They sell.7 m of the total length of their track. What length of track is left? 0. The Robinson family ( adults and children) are members of Parkmead Leisure Centre. SWIMMING PRICES Members Non-Members Adults.0.00 Children.0.0 How much in total do the Robinson family have to pay for a swim? How much less do the Robinson family pay as members for a swim, than they would if they were non-members? A family ticket for membership costs. What is the minimum number of times that the Robinson family would have to go swimming if they were to save money on their family ticket?. Fatima is making a shelf unit as shown. She needs three pieces of wood, each of length. m, for the shelves. She needs two pieces of wood, each of length 0.9 m, for the ends. The wood is sold only in 3 m lengths. Calculate how many 3 m lengths Fatima needs to buy.. m 0.9 m 69
. A sports shop keeps information about sports shoes on a database. Part of this database is shown below. Model Manufacturer Cost Flyer Tiger 39.99 Racer Cheetah 37.9 Runner Cheetah 3.99 Strider Tiger 8.99 Blinder Lion 33.9 Sprinter Leopard 9.99 Write down the name of the manufacturer of the cheapest shoe. How much dearer is the Strider than the Racer? (LON) 3. Six girls competed in the long jump at their school Sports Day. Their best jumps were as follows. Anne 6.08 m Donna 6. m Beth.93 m Emma.98 m Candy.87 m Fatima.98 m Fatima finished in second place. Write down a possible length for Fatima's jump. Arrange the six competitors in order of merit. Write down the length of Anne's jump in centimetres. 6. Multiplying and Dividing with Decimals. Without using a calculator, find. 0. 7 00 3. 0 (d) 9. 000 (e). 00 (f) 07. 0 (g) 9 00 (h) 7. 93 000 (i). 00 (j) 0. 00 (k) 0. 009 000 (l) 0. 078 00. Without using a calculator, find 7. 0. 0 76. 9 00 (d) 00. 0 (e) 00. 00 (f) 99 00 (g) 6. 00 (h) 978 000 (i) 978 00 (j) 7. 9 00 (k) 0. 09 00 (l) 000 0 000 70
3. The Williamson family went into a café. The table shows what they ordered. Cost. p Three cans of cola at 63 pence each. 89 Two cups of tea at pence each Five buns at 3 pence each Total cost Copy and complete the table. Mr. Williamson paid the bill with a 0 note. How much change did he get? (LON). ORANGES for.0 ORANGES 0 for These notices were seen on two market stalls. At which stall was the price of one orange cheaper and by how much?. Fencing rails are 3.9 metres long. 3.9 m How many rails are needed for a fence 00 metres long? 6. Tom earns a basic weekly wage of 80 for 36 hours work. How much does Tom earn for one hour at the basic rate? Overtime pay is one and a half times the basic rate. How much is Tom paid for one hour of overtime? Overtime is paid for each hour over the basic 36 hours. How much does Tom earn if he works 3 hours in one week? 7
7. Jane's classroom is rectangular. She measures the length and width of the floor. The length is 6.73 m. The width is.6 m. Calculate the area of the classroom floor. Write down all the figures in the answer shown on your calculator. (i) The classroom is to be carpeted. Give your answer to part to an appropriate degree of accuracy. (ii) Explain why you chose this degree of accuracy. 6.3 Fractions and Decimals. Write each of the following correct to decimal place. 3..67 38.8 (d) 9.9 (e) 8.0 (f).97 (g) 0. (h) 0.06. Write each of the following correct to decimal places. 0.089 6.3 0.80 (d).989 (e).999 (f) 0.007 (g).00 (h).36 3. Write all the numbers in Question, correct to (i) significant figures (ii) significant figure.. Write each of the following as exact decimal equivalents. 3 8 (d) 7 8 (e) (f) 3 (g) 8 (h) 8. Write each of the following as decimals, correct to 3 decimal places. 3 6 7 (d) (e) 9 (f) 3 (g) 6 (h) 7 7
6. Copy and complete the table below, putting on the equivalent fractions, decimals and percentages. Proportion Fraction Decimal Percentage one tenth 0 % 0.3 three eighths 0.6 three quarters 6. Long Multiplication and Division. Without using a calculator, find 7 3 6 33 (d) 3 0 (e) 7 (f) 7 (g) 7 7 (h) 3 7 (i) 90. Without using a calculator, find 0 0 0 008 8 (d) 3 (e) 96 3 (f) 76 (g) 7 3 (h) 33 9 (i) 89 99 3. A Maths teacher buys 9 text books, costing 3.8 each. Without using a calculator, work out the exact total cost. 73
. A group of teachers wins.7 milion on the National Lottery. Without using a calculator, find out how much each gets in s if the money is shared equally.. 7 tickets cost.. If they all cost the same, find, without using a calculator, the cost of one ticket. 6. Estimating Answers. Express each of the following correct to 3 significant figures: 96.63 36..90 (d) 0.00 68 (e) 0.9 (f) 0.000 60 8 (g) 0.00 73 (h).98 (i) 6.98. Write each of the following correct to the number of significant figures (s.f.) indicated. 308.637 ( s.f.) 0.099 8 ( s.f.) 0.6 (3 s.f.) (d) 0.00 307 ( s.f.) 3. Write 3.00 7 correct to s.f. s.f. s.f.. Nigel, Ali and Sue were given ten calculations to do. The following table shows their answers. For each calculation, only one of the three obtained the correct answer. By working out an estimate for each question, decide who was correct in each calculation. Question Nigel's answer Ali's answer Sue's answer.0.9.98.98 6.38 0.99 6.7 6.33 3.36.633.8 0. 6.3 9.9 89. (d) 33.6 3. 8..6. (e) 3. 8.0... (f) 7. 7. 0.. 36.0 (g) 7.08.66.68.08.8 (h) 76.6 7.6.6 8.6. (i).7 8. 0.8 07.9 0.7 (j) 8.3 0.97.7 6.6 8.6 7
. Without finding an exact answer: which of the following is nearest in value to 696. + 7. + 7. + 68.?.7, 8.09, 90.73 or.86 which of the following is nearest in value to 3. 300 3. 3? 7, 87, 870 or 70 which of the following is nearest in value to 9 7 + 0? 8, 67,.8 or 6.7 6. Estimate, correct to significant figure, the value of 0. 9.. 7. Express each number correct to significant figure and work out an estimate to 9. 7 9. 7.. Use your calculator to evaluate 9. 7 9. 7. correct to significant figures. 8. Bottles of mineral water cost 39 p each. Estimate the cost of bottles. Show how you obtained your estimate. Without using a calculator, work out the exact cost of bottles of mineral water at 39 p each. 9. Charlie has to work out. 39... He uses a calculator and gets.88 for his answer. Saeeda works out an approximate answer for the question. She knows that Charlie's answer must be wrong. (i) Write down approximate values for., 3.9 and.. (ii) Use these approximations to find a rough answer to Charlie's calculation. What is the mistake in Charlie's answer? 7
0. The rectangular glass tank shown in the diagram contains litre (000 cm 3 of water. d cm Not to scale.63 cm 9. cm Sanjay wanted to find the depth (d cm) of the water. He multiplied.63 by 9. on his calculator and wrote down the answer. He then divided 000 by this answer. Explain how you could use your calculator to find the depth without writing down the answer to. 63 9.. Work out the depth of the water, and write down all the figures on your calculator display. 6.6 Using Brackets and Memory on a Calculator. Use a calculator to evaluate each of the following: 80 96 + 09 33 ( ) ( ) ( + ) ( ) ( + ) [( + ) ( )] ( ) + ( ) 33 + 8 7 (d) + 696 (e) 83 69 9 (f) 70 9 (g) 777 7 8 78 7 [ ] (h) 3330 90 798 869 70. For each of the following expressions, evaluate, giving your answer correct to decimal places; express each number correct to the nearest whole number and give an estimate to check your calculations. ( ) (i) 6. + 39.. (ii) 6. + 39.. (iii) 3. 3 0. 6 (iv). 08. 6.. (v). 8. 3. ( ) (vi) 9. + 36. 9. 76
3. Use your calculator to work out the value of 608. 97. 8 + 37 ( ) Write down the full calculator display. (i) Write down a calculation that could be done mentally to check the answer to part using numbers rounded to one significant figure. (ii) Write down the answer to your calculation in part (i).. Work out: 06.. 78 86 7.. Gabriel buys a packet of 8 biscuits. The packet weighs 8 g. Gabriel wants to calculate the weight of one of these biscuits. He presses the following buttons on his calculator. 8 8 = Explain what is wrong with his calculation. Calculate the weight of one of these biscuits. Give your answer to the nearest gram. Gabriel checks his answer without using a calculator. Show how you can use approximation to check that his answer is of the right order. You must show all your working. 6.7 Upper and Lower Bounds. Write down the upper and lower bounds for each of the following measurements. 6 g 3.0 litres.3 metres (d).6 km (e) 7.8 metres (f) 8. kg (g) 7. seconds (h) 0. mm (i).9 cm. Find the upper and lower bounds for each of the calculations shown below, assuming the dimensions given are subject to rounding errors. The perimeter of a rectangle 6 cm by 8 cm. The area of a rectangle 6 cm by 8 cm. The perimeter of an octagon of side mm. (d) The volume of a cube of edge length 96 mm. (e) The total weight of objects, each weighing.6 kg. 77
3. Angela measures the lengths of some sticks to the nearest centimetre. She arranges them in groups. The length of the sticks in the shortest group is cm, to the nearest centimetre. (i) (ii) What is the smallest possible length for a stick in this group? What is the smallest possible length for a stick which is not in this group? Angela measures the lengths of some other sticks. She records the length of one of these sticks as. cm, to the nearest tenth of a centimetre. What is the smallest possible length of this stick?. Sections of a railway line are measured to the nearest metre as either 00 m or 80 m. What are the bounds on the total length of sections, consisting of eight 00 m sections and seven 80 m sections?. The area of a rectangle is. square centimetres, correct to decimal place. The length of this rectangle is 8.3 centimetres, correct to decimal place. From this information, write down (i) the largest value (ii) the smallest value that the length of the rectangle could have. Use your answers in to calculate the largest possible width of the rectangle. (NEAB) 6. The formula S F = is used in engineering. A F = 89, correct to 3 significant figures A = 93., correct to 3 significant figures. For the value of F, write down (i) the upper bound (ii) the lower bound. For the value of A, write down (i) the upper bound (ii) the lower bound. Calculate (i) the upper bound (ii) the lower bound for the value of S for these values of F and A. Write down all the figures on your calculator display. (d) Write down this value of S correct to an appropriate number of significant figures. (LON) 78