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.

Estimating a restaurant bill

Three friends order meals costing $\displaystyle \$18.90$ , $\displaystyle \$23.40$ and $\displaystyle \$31.70$ . 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 $\displaystyle \frac{78.3 \times 3.14}{0.489}$ .

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

Estimate $778 + 695$ by rounding each number to 1 significant figure.

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778 = 800

(to 1 s.f.)

695 = 700

(to 1 s.f.)

800 + 700 = 1500

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

A jacket in Tokyo costs 8900 yen. The exchange rate is 1 yen = S$0.0087. Estimate the price in Singapore dollars.

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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 leather bag costs Rp 700 000. The conversion rate is Rp 1000 = S$0.09. Without using a calculator, estimate the price in S$.

Show solution▾

Given: Rp 1000 = S$0.09

Rp 10 000 = S$0.90

S$0.90 = S$1 (to the nearest dollar)

Rp 700 000 = 70 × Rp 10 000

= 70 × S$1

Estimated price = S$70

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Count a small sample, then scale up: multiply by however many times the sample fits into the whole.