Worksheets for GCSE Mathematics Accuracy & Rounding Mr Black's Maths Resources for Teachers Number
Accuracy & Rounding Worksheets Contents Differentiated Independent Learning Worksheets Rounding to the nearest ten, hundred and thousand Page 20 Rounding to a given decimal place Page 30 Rounding to a given significant figure Page 40 Estimating solutions Page 50 Limits of accuracy in measurement Page 70 Limits of accuracy in calculations Page 80 Solutions Rounding to the nearest ten, hundred and thousand Page 90 Rounding to a given decimal place Page 10 Rounding to a given significant figure Page 11 Estimating solutions Page 12 Limits of accuracy in measurement Page 13 Limits of accuracy in calculations Page 14 2
Rounding to the nearest 10, 100 and 1000 Q1. Round each of these numbers to the nearest 10. a) 56 b) 37 c) 29 d) 45 e) 68 f) 24 g) 53 h) 86 i) 145 j) 41 k) 831 l) 527 Q2. Round each of these numbers to the nearest 100. a) 382 b) 423 c) 650 d) 790 e) 796 f) 8405 g) 995 h) 9108 Q3. Round each of these numbers to the nearest 1000. a) 1541 b) 59652 c) 22269 d) 51128 e) 44642 f) 3759 g) 89174 h) 34694 a) b) c) Here are the crowd figures for the first game of a football season. Round each number to the nearest 100. Round each number to the nearest 1000. Which do you think gives the better estimate? Explain your decision. Q5. From each set of numbers decide which the odd one out is. Explain your decision. a) 26 22 30 34 29 b) 153 214 197 234 251 c) 6580 7153 7200 7602 6890 d) 36150 36145 36158 36148 36154 3
Rounding to a Decimal Place Q1. Write down all the numbers in the box that round to 0.5 to one decimal place. 0.5386 0.4478 0.464 0.4865 0.58 0.5858 0.51 0.56 0.45 0.5104 Q2. Round the following numbers to one decimal place. a) 23.695 b) 58.311 c) 1.706 d) 72.093 e) 33.13 f) 17.721 g) 75.381 h) 66.502 i) 58.024 j) 63.256 k) 0.015 l) 97.068 Q3. Round the following numbers to two decimal places. a) 1.534 b) 543.482 c) 69.266 d) 77.935 e) 0.039 f) 0.05728 g) 0.00615 h) 0.09520 Round these numbers to the number of decimal places (d.p.) specified. a) 0.01903 to 2 d.p. b) 0.05607 to 2 d.p. c) 0.07302 to 1 d.p. d) 0.098 to 2 d.p. e) 0.075 to 1 d.p. f) 0.06397 to 3 d.p. g) 0.01752 to 3 d.p. h) 0.0765 to 3 d.p. i) 0.04345 to 4 d.p. Q5. Which of the following numbers is the odd one out? Explain your decision. 0.2456 0.2501 0.248 0.2550 0.2540 Q6. Use written methods to calculate the following giving your answers to two decimal places. a) 1.524+5.72 b) 6.355 0.17 c) 0.264 0.0115 d) 2.48 6.27 e) 4.812 f) 5.48 0.42 Q7. Use your calculator to evaluate the following. Round each answer to two decimal places. d) e) f) 4
Rounding to a Significant Figure Q1. Round the following numbers to 1 significant figure. a) 60.3 b) 98.38 c) 65.204 d) 96.504 e) 879.884 f) 645.233 g) 0.091968 h) 0.040057 Q2. Round the following numbers to 2 significant figures. a) 25.2 b) 93.52 c) 3.448 d) 74.286 e) 300.243 f) 779.055 g) 0.053407 h) 0.010415 Q3. Round the following numbers to the number of significant figures (s.f.) indicated. a) 51.124 - to 2 s.f. b) 935.338 - to 1 s.f. c) 0.016113 - to 3 s.f. d) 0.076242 - to 3 s.f. e) 800.085 - to 1 s.f. f) 481.155 - to 2 s.f. g) 0.053832 - to 1 s.f. h) 0.052245 - to 4 s.f. i) 178.218 - to 1 s.f. j) 79.458 - to 2 s.f. k) 0.048647 - to 4 s.f. l) 0.047152 - to 2 s.f. The table shows the population of the six most populated countries. Round each population to two significant figures. Q5. For each set decide which number is the odd one out. Explain your decision. a) 25 32 36 31 27 b) c) d) 458.3 464.65 452.01 462.99 456 0.085 0.8543 0.845 0.8541 0.854 3.12 3.14 3.06 3.09 3.16 Q6. Round each number to 1 significant figure to estimate the value of the following calculations. 5
Estimating Solutions Q1. Estimate the value of the following calculations. g) h) i) j) k) l) Q2. Use a suitable estimate to check each answer shown. If the answer is incorrect, work out the correct approximation. a) b) c) d) =6.724 e) f) Q3. Estimate the value of the following calculations. Estimate the square roots to these numbers. a) 17 b) 26 c) 5 d) 915 Q5. Estimate the value of the following calculations. d) e) f) Q6. Match the calculation with the approximate solution. 6
Limits of Accuracy Q1. Write down the limits of accuracy for the following measurements. a) 5 cm measured to the nearest cm. b) 8 kg measured to the nearest kg. c) 20 minutes measured to the nearest minute. d) 54 measured to the nearest. e) 870 km measured to the nearest km. f) 106 mm measured to the nearest mm. g) 100 km measured to the nearest km. h) 3 m measured to the nearest cm. Q2. Match the measurement to the limits of accuracy with the measurement. 4 (nearest integer) 4.5 (nearest tenth) 4.05 (nearest hundredth) 4.50 (nearest hundredth) Q3. Write down the upper and lower bounds for each of the following values which are rounded to the accuracy stated. a) 6 (nearest integer) b) 40 (nearest 10) c) 1300 (nearest 100) d) 863 (nearest integer) e) 5.7 (1 decimal place) f) 0.6 (1 decimal place) g) 80 (1 significant figure) h) 12.93 (2 decimal places) i) 0.08 (1 significant figure) j) 12.5 (3 significant figures) k) 9.0(1 decimal place) l) 800 (1 significant figure) m) 45000 (nearest 1000) n) 1.48 (2 decimal places) o) 0.04 (1 significant figure) To the nearest hundred there are 600 students on roll at Eversmith School and 900 students on roll at Goldburn College. The two schools intended to merge to create a Goldsmith Academy. Write down the limits of accuracy for the number of students on roll at the new Goldsmith Academy. Q5. a) b) The length and width of a rectangle are measured as 8 cm and 12 cm each to the nearest cm. Calculate the limits of accuracy for the perimeter of the rectangle. Calculate the limits of accuracy for the area of the rectangle. 7
Calculations with Limits of Accuracy Q1. Calculate the limits of accuracy for the perimeter and area of the following shapes. a) Measurements are rounded to the nearest cm. b) Measurements are rounded to the nearest cm. c) Measurements are rounded to the nearest mm. d) Measurements are rounded to the nearest tenth of a cm. Q2. Substitute upper and lower bounds of the following values into the expressions to calculate the limits of accuracy. (1 sig. fig.) (1 d. p.) (2 sig. fig.) (2 d.p.) a) b) c) d) Q3. a) b) c) A stopwatch records the time for the winner of a 200-metre race as 24.7 seconds, measured to the nearest one-tenth of a second. What are the greatest and least possible times of the winner? The length of the 200-metre track is correct to the nearest 1 m. What are the greatest and least possible lengths of the track? What s the fastest possible average speed of the winner with a time of 24.7 seconds in the 200- metre race? to 2 decimal places 9.485 to 3 decimal places. By considering bounds, work out the value of to a suitable degree of accuracy. You must show all your working and give a reason for your final answer. 8
Solutions Rounding to the nearest 10, 100 and 1000 Q1. a) 60 b) 40 c) 30 d) 50 e) 70 f) 20 g) 50 h) 90 i) 150 j) 40 k) 830 l) 530 Q2. a) 400 b) 400 c) 700 d) 800 e) 800 f) 8400 g) 1000 h) 9100 Q3. a) 2000 b) 60000 c) 22000 d) 51000 e) 45000 f) 4000 g) 89000 h) 35000 Q5. a) 22 is the odd one out since the rest round to 30 to the nearest 10. b) 251 is the odd one out since the rest round to 200 to the nearest 100. c) 7602 is the odd one out since the rest round to 7000 to the nearest 1000. d) 36158 is the odd one out since the rest round to 36150 to the nearest 10. 9
Rounding to a Decimal Place Q1. Q2. 0.5386 0.4478 0.464 0.4865 0.58 0.5858 0.51 0.56 0.45 0.5104 a) 23.7 b) 58.3 c) 1.7 d) 72.1 e) 33.1 f) 17.7 g) 75.4 h) 66.5 i) 58.0 j) 63.3 k) 0.0 l) 97.1 Q3. a) 1.53 b) 543.48 c) 69.27 d) 77.94 e) 0.04 f) 0.06 g) 0.01 h) 0.10 a) 0.02 b) 0.06 c) 0.1 d) 0.10 e) 0.175 f) 0.064 g) 0.018 h) 0.077 i) 0.0435 Q5. 0.2550 is the odd one out as the others round to 0.25 to 2 d.p. Q6. Q7. 10
Rounding to a Significant Figure Q1. a) 60 b) 100 c) 70 d) 100 e) 800 f) 600 g) 0.09 h) 0.04 Q2. a) 25 b) 94 c) 3.4 d) 74 e) 300 f) 780 g) 0.053 h) 0.010 Q3. a) 51 b) 900 c) 0.0161 d) 0.0762 e) 800 f) 480 g) 0.05 h) 0.05225 i) 200 j) 79 k) 0.04864 l) 0.047 Q5. a) 36 as the others round to 30 to 1 significant figure b) 452.01 as the others round to 460 to 2 significant figures. c) 0.085 as the others round to 0.85 to 2 significant figures. d) 3.16 as the others round to 3.1 to 2 significant figures. Q6. 11
Estimating Solutions Q1. g) h) i) j) k) l) Q2. a) Correct b) Incorrect (18.3235) c) Correct d) Incorrect (67.24) e) Correct f) Incorrect (0.002145) Q3. a) 4 b) 5 c) 2 d) 30 Q5. Q6. 12
Limits of Accuracy Q1. a) b) Q2. c) d) 53.50 e) 865 km 875 km f) 105.5 mm g) 95 km 105 km h) 300.5 cm 4 (nearest integer) 4.5 (nearest tenth) 4.05 (nearest hundredth) 4.50 (nearest hundredth) Q3. a) LB = 5.5, UB = 6.5 b) LB = 35, UB = 45 c) LB = 1250, UB = 1350 Q5. a) b) d) LB = 862.5, UB =863.5 e) LB = 5.65, UB = 5.75 f) LB = 0.55, UB = 0.65 g) LB = 75, UB = 85 h) LB = 12.925, UB = 12.935 i) LB = 0.075, UB = 0.085 j) LB = 12.45, UB = 12.55 k) LB = 8.95, UB = 9.05 l) LB = 750, UB = 850 m) LB = 44500, UB = 45500 n) LB = 1.475, UB = 1.485 o) LB = 0.035, UB = 0.045 13
Calculations with Limits of Accuracy Q1. a) b) c) d) Q2. a) LB = 150.0385, UB = 250.0395 b) LB = 8.2755, UB = 8.2865 c) LB = 1242.6, UB = 2076.7 d) LB = 115.19, UB = 120.779 Q3. a) LB = 24.65 seconds, UB = 24.75 seconds b) LB = 199.5 m, UB = 200.5 m c) Maximum Speed = 8.1339 m/sec Any answer within the range. Ranges must be shown. 14