Sec 1 G2 Maths Approximation and estimation worksheet with answers
A free Sec 1 G2 Maths worksheet on approximation and estimation: 7 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.
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Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.
Section A
1
(a)By writing each number correct to 1 significant figure, estimate the value of 9.42×11.7.
Answer (a)[1]
(b)By writing each number correct to 1 significant figure, estimate the value of 81.6×2.14.
Answer (b)[1]
2
(a)Write 0.000194 correct to 2 significant figures.
Answer (a)[1]
(b)State the number of significant figures in 1204.
Answer (b)[1]
3
Use a calculator to evaluate 9.4−1.9361.2+2.32, giving your answer correct to 3 significant figures.
Answer[2]
4
(a)The mass of a bag of rice is 0.8 kg, correct to 1 decimal place. Complete the statement: the actual mass of the bag of rice is less than …… kg.
Answer (a)kg[1]
(b)The number of books in a library is 17080, correct to 4 significant figures. Find the smallest and the largest possible number of books.
Answer (b)[3]
Section B
5
(a)(i)Write 0.2048 correct to 1 significant figure.
Answer (a)(i)[1]
(a)(ii)State the number of significant figures in 3.004.
Answer (a)(ii)[1]
(b)(i)Write 98765 correct to the nearest 1000.
Answer (b)(i)[1]
(b)(ii)Use a calculator to evaluate 717, giving your answer correct to 3 decimal places.
Answer (b)(ii)[1]
6
(a)(i)Write 0.07071 correct to 2 significant figures.
Answer (a)(i)[1]
(a)(ii)Write 0.00351 correct to 1 significant figure.
Answer (a)(ii)[1]
(b)Use a calculator to evaluate 2.62−1.457.25+50, giving your answer correct to 3 significant figures.
Answer (b)[2]
(c)(i)The time taken by a runner to complete a race is 9.7 s, correct to 1 decimal place. Write down the least possible time taken.
Answer (c)(i)s[1]
(c)(ii)By writing each number correct to 1 significant figure, 2.47×38.3 is estimated to be 80. Express the difference between this estimate and the exact value as a percentage of the exact value, giving your answer correct to 3 significant figures.
Answer (c)(ii)%[3]
7
(a)(i)The length of a rod is 37.5 cm, correct to 1 decimal place. Given that the actual length of the rod is l cm, write down the range of possible values of l.
Answer (a)(i)[1]
(a)(ii)The mass of a bag of rice is 12 kg, correct to the nearest kg. Given that the actual mass of the bag of rice is m kg, write down the range of possible values of m.
Answer (a)(ii)[1]
(b)(i)State the number of significant figures in 49.00.
Answer (b)(i)[1]
(b)(ii)State the number of significant figures in 0.00602.
Answer (b)(ii)[1]
(c)(i)Hui Min uses a calculator and obtains 81.6×2.14=17.4624. By writing each number correct to 1 significant figure, state whether this answer is reasonable.
Answer (c)(i)[2]
(c)(ii)By rounding each number to the nearest whole number, estimate the value of 15.7×4.75. Show your working clearly.
Answer (c)(ii)[2]
END OF PAPER
Answers and worked solutions
Question 1
(a)Answer: =90[1]
9.42×11.7≈9×10=90
(b)Answer: =160[1]
81.6×2.14≈80×2=160
Question 2
(a)Answer: 0.000194=0.00019 (2 s.f.)[1]
The 3rd significant figure is 4.It is 4 or less, so round down.0.000194=0.00019 (2 s.f.)
(b)Answer: 1204 has 4 significant figures.[1]
The number starts with a non-zero digit, so start counting from the first digit.A zero between two non-zero digits is significant.1204 has 4 significant figures.
(b)Answer: Largest=17084 (17085 itself rounds up to 17090).[3]
17080 to 4 significant figures is rounded to the nearest 10.Half of 10 is 5.Smallest=17080−5Smallest=17075Largest=17080+5−1Largest=17084 (17085 itself rounds up to 17090).
Question 5
(a)(i)Answer: 0.2048=0.2 (1 s.f.)[1]
The 2nd significant figure is 0.It is 4 or less, so round down.0.2048=0.2 (1 s.f.)
(a)(ii)Answer: 3.004 has 4 significant figures.[1]
The number starts with a non-zero digit, so start counting from the first digit.A zero between two non-zero digits is significant.3.004 has 4 significant figures.
(b)(i)Answer: 98765=99000 (nearest 1000)[1]
The deciding digit is 7.It is 5 or more, so round up.98765=99000 (nearest 1000)
(b)(ii)Answer: =2.429 (3 d.p.)[1]
717=2.42857…=2.429 (3 d.p.)
Question 6
(a)(i)Answer: 0.07071=0.071 (2 s.f.)[1]
The 3rd significant figure is 7.It is 5 or more, so round up.0.07071=0.071 (2 s.f.)
(a)(ii)Answer: 0.00351=0.004 (1 s.f.)[1]
The 2nd significant figure is 5.It is 5 or more, so round up.0.00351=0.004 (1 s.f.)
The number starts with a non-zero digit, so start counting from the first digit.A zero at the end of a decimal is significant: it shows the accuracy.49.00 has 4 significant figures.
(b)(ii)Answer: 0.00602 has 3 significant figures.[1]
The zeros before the first non-zero digit only show the place value: they are not significant.A zero between two non-zero digits is significant.0.00602 has 3 significant figures.
(c)(i)Answer: NO[2]
81.6×2.14≈80×2=16017.4624 is about a tenth of the estimate 160, so the answer is not reasonable: the decimal point is in the wrong place.