Sec 1 Maths · Approximation and estimation

Estimation questions with answers

Practice questions on estimation, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

By writing each number correct to 1 significant figure, estimate the value of $0.0487 \times 61.2$ .

Step 1 of 2

Round each number to 1 significant figure

0.0487 \times 61.2 \approx 0.05 \times 60

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Questions

Question 1Estimate a product
By writing each number correct to 1 significant figure, estimate the value of $396 \times 0.214$ .
Show the worked solution
1. Step 1: Round each number to 1 significant figure $396 \times 0.214 \approx 400 \times 0.2$
2. Step 2: Work out the estimate $= 80$
Question 2Estimate a fraction
By writing each number correct to 1 significant figure, estimate the value of $\dfrac{7.83 \times 19.6}{4.21}$ .
Show the worked solution
1. Step 1: Round each number to 1 significant figure $\dfrac{7.83 \times 19.6}{4.21} \approx \dfrac{8 \times 20}{4}$
2. Step 2: Work out the top, then divide (no calculator needed) $= \dfrac{160}{4}$ $= 40$
Question 3Is the calculator answer reasonable?
Hui Min uses a calculator and obtains $7.12 \times 28.9 = 20.5768$ . By writing each number correct to 1 significant figure, state whether this answer is reasonable.
Show the worked solution
1. Step 1: Round each number to 1 significant figure $7.12 \times 28.9 \approx 7 \times 30$
2. Step 2: Work out the estimate $= 210$
3. Step 3: Compare: a reasonable answer is close to the estimate $20.5768$ is about a tenth of the estimate $210$ , so the answer is not reasonable: the decimal point is in the wrong place.
Question 4Is the estimate more or less than the exact value?
Kumar estimates the value of $4.96 \times 0.287$ by writing each number correct to 1 significant figure. Without finding the exact value, explain whether the estimate is greater than or less than the exact value.
Show the worked solution
1. Step 1: Round each number to 1 significant figure: did it go up or down? $4.96 \rightarrow 5$ is rounded up; $0.287 \rightarrow 0.3$ is rounded up.
2. Step 2: A product goes up when either number goes upBoth numbers were rounded up, so the estimate is greater than the exact value.
Question 5Round to the nearest whole number, then estimate
By rounding each number to the nearest whole number, estimate the value of $\dfrac{11.8 \times 3.15}{6.17}$ . Show your working clearly.
Show the worked solution
1. Step 1: Round each number to the nearest whole number (look at the first decimal place) $\dfrac{11.8 \times 3.15}{6.17} \approx \dfrac{12 \times 3}{6}$
2. Step 2: Work it out without a calculator $= \dfrac{36}{6}$ $= 6$

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Notes: Approximation and estimation Worksheet with answers (PDF)

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Questions

Question 1Estimate a product

By writing each number correct to 1 significant figure, estimate the value of $396 \times 0.214$ .

Show the worked solution

Step 1: Round each number to 1 significant figure $396 \times 0.214 \approx 400 \times 0.2$
Step 2: Work out the estimate $= 80$

Question 2Estimate a fraction

By writing each number correct to 1 significant figure, estimate the value of $\dfrac{7.83 \times 19.6}{4.21}$ .

Show the worked solution

Step 1: Round each number to 1 significant figure $\dfrac{7.83 \times 19.6}{4.21} \approx \dfrac{8 \times 20}{4}$
Step 2: Work out the top, then divide (no calculator needed) $= \dfrac{160}{4}$ $= 40$

Question 3Is the calculator answer reasonable?

Hui Min uses a calculator and obtains $7.12 \times 28.9 = 20.5768$ . By writing each number correct to 1 significant figure, state whether this answer is reasonable.

Show the worked solution

Step 1: Round each number to 1 significant figure $7.12 \times 28.9 \approx 7 \times 30$
Step 2: Work out the estimate $= 210$
Step 3: Compare: a reasonable answer is close to the estimate $20.5768$ is about a tenth of the estimate $210$ , so the answer is not reasonable: the decimal point is in the wrong place.

Question 4Is the estimate more or less than the exact value?

Kumar estimates the value of $4.96 \times 0.287$ by writing each number correct to 1 significant figure. Without finding the exact value, explain whether the estimate is greater than or less than the exact value.

Show the worked solution

Step 1: Round each number to 1 significant figure: did it go up or down? $4.96 \rightarrow 5$ is rounded up; $0.287 \rightarrow 0.3$ is rounded up.
Step 2: A product goes up when either number goes upBoth numbers were rounded up, so the estimate is greater than the exact value.

Question 5Round to the nearest whole number, then estimate

By rounding each number to the nearest whole number, estimate the value of $\dfrac{11.8 \times 3.15}{6.17}$ . Show your working clearly.

Show the worked solution

Step 1: Round each number to the nearest whole number (look at the first decimal place) $\dfrac{11.8 \times 3.15}{6.17} \approx \dfrac{12 \times 3}{6}$
Step 2: Work it out without a calculator $= \dfrac{36}{6}$ $= 6$