A delivery firm works out its cost for each parcel using the calculation below. \[\frac{58.3 \times 41.7}{0.19}\] By writing each number correct to 1 signif...
Question 1 Report
A delivery firm works out its cost for each parcel using the calculation below.
\[\frac{58.3 \times 41.7}{0.19}\]By writing each number correct to 1 significant figure, estimate the value of this calculation. (2)
Answer Details
Estimation replaces every number by its value to 1 significant figure, so that the arithmetic can be done without a calculator while staying close to the true size of the answer.
- To 1 significant figure, 58.3 becomes 60, 41.7 becomes 40, and 0.19 becomes 0.2. Note that the leading zeros in 0.19 are not significant, so the first significant figure is the 1, and the following 9 rounds it up to 0.2. [1]
- \(\frac{60 \times 40}{0.2} = \frac{2400}{0.2} = 12\,000\). [1]
Dividing by 0.2 is the same as multiplying by 5, since \(0.2 = \frac{1}{5}\), which is why the answer grows rather than shrinks. Dividing by a number smaller than 1 always increases the result, and expecting a decrease is the usual misconception here.
The exact value is 12 792.8, so the estimate is the right order of magnitude, which is exactly what an estimate is for. Round every number first and only then carry out the arithmetic, since rounding the final answer instead does not demonstrate the estimation method.
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