3.5Estimation in Real-World Contexts

Round every figure to 1 s.f., compute in your head, and you have a check on any calculator answer.

Three friends order meals costing $\$18.90$ , $\$23.40$ and $\$31.70$ . Estimate the total bill before GST.

Show solution▾

18.90 = 20

23.40 = 20

31.70 = 30

(to 1 s.f.)

Estimate:

20 + 20 + 30 = \$70

(Actual:

\$74

. Our estimate is reasonable.)

Without a calculator, estimate $\frac{78.3 \times 3.14}{0.489}$ .

Show solution▾

78.3 = 80

3.14 = 3

0.489 = 0.5

(each to 1 s.f.)

Estimate

\approx \frac{80 \times 3}{0.5} = \frac{240}{0.5} = 480

Now you try

A question on this, marked as you go, with the working shown. No account needed.

The same move covers currency, value for money, and scaling from a sample.

A jacket in Tokyo costs 8 900 yen. The exchange rate is 1 yen = S$0.0087. Estimate the price in Singapore dollars.

Show solution▾

8900 = 9000

and

0.0087 = 0.009

(to 1 s.f.)

Estimate:

9000 \times 0.009 =

S$81.

(Actual:

8900 \times 0.0087 =

S$77.43. Our estimate is in the right ballpark.)

Now you try

A question on this, marked as you go, with the working shown. No account needed.

Count a small sample, then scale up to estimate a large total.

Scaling formula

\text{Estimated total} = \text{sample count} \times \dfrac{\text{total area}}{\text{sample area}}

Approximation and Estimation