Decimals and Fractions 4
Estimating Answers

If you do a calculation such as

you need to use a calculator to find the answer. This section looks at ways of estimating the answers to calculations such as this, and giving answers to a specified accuracy.

Worked Examples

1

Give each of the following numbers to

(i) 2 significant figures (2 s.f.) (ii) 1 decimal place (1 d.p.)
(a)
17.47 Show me ≈ 17  to 2 s.f. ≈ 17.5  to 1 d.p.
(b)
0.0784 Show me ≈ 0.078  to 2 s.f. ≈ 0.1  to 1 d.p.
(c)
4.96 Show me ≈ 5.0  to 2 s.f. ≈ 5.0  to 1 d.p.
2

Estimate the answers to each of the following problems.

(a)

18.42 × 3.76

Show me
18.42 × 3.76 ≈ 20 × 4
≈ 80
(b)

Show me
≈
≈ 12
(c)

Show me
≈
≈
≈ 10

Exercises

Write each of the following numbers correct to 1 significant figure.

(a)
47.316
(b)
18.45
(c)
27.65
(d)
9.632
(e)
15.01
(f)
149.32
(g)
62.84
(h)
0.176
(i)
0.039 4
(j)
1.964
(k)
21.87
(l)
1.849

Estimate the answers to the following problems:

(a)
6.74 × 8.31
(b)
4.35 × 12.46
(c)
236 × 4.321
(d)
16.67 × 3.21
(e)
5.92 × 105.3
(f)
16.78 × 32.51
(g)
(h)
(i)
(j)
(k)
(l)
Now, using a calculator, find the answer to each problem in Question 2, giving your answer to 4 significant figures. In each case compare your answers and estimates.

Estimate the answers to each of the following calculations.

(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)

Drivers at a motor racing circuit complete practice laps in times of 130.21, 131.43 and 133.62 seconds. The length of the circuit is 5214 metres.

(a)

Estimate the average speed of the drivers. (Average speed = )

About ms−1
(b)

Find their speeds correct to 2 decimal places.

ms−1, ms−1, ms−1

(a)

Write down the numbers you could use to get an approximate answer to

59 × 32

×
(b)

Write down your approximate answer.

(c)

Using a calculator find the difference between your approximate answer and the exact answer.