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Rounding Errors Impact

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Rounding Errors Impact

Solve each problem and show your working. Keep full precision during calculations, then round only when the question asks you to. Unless stated otherwise, give percentage errors to 2 decimal places.

Precision in practice

A surveying team is checking measurements for a new walking track. Small rounding differences can matter when measurements are used repeatedly.

1.A track segment is measured as 2.456 km. Round this measurement to the nearest 0.1 km. Explain which digit determines whether the tenths digit stays the same or increases.

2.The survey software rounds 2.456 km to 2.5 km. On the number line, mark the exact measurement and the rounded measurement. Which value is greater?

3.A gravel order is calculated as 98.76 tonnes, then reported as 99 tonnes. Calculate the absolute error in tonnes.

4.Using the gravel order values 98.76 tonnes (exact) and 99 tonnes (reported), calculate the relative error and percentage error. Use the exact value as the denominator.

5.A fuel estimate is 45.82 L, but the display rounds it to 46 L. Choose the correct pair of errors.

Absolute error 0.18 L; percentage error about 0.39%
Absolute error 0.18 L; percentage error about 3.9%
Absolute error 0.82 L; percentage error about 1.79%
Absolute error 1.82 L; percentage error about 0.39%

6.A 1.8 m length of edging and a 180 m length of path are each rounded to the nearest metre. Which measurement has the larger maximum possible percentage error? Explain briefly.

7.A calculator gives 7.3486 m for a measurement. Match each reporting precision to its rounded value.

Nearest metre
Nearest 0.1 m
Nearest 0.01 m

7 m
7.35 m
7.3 m

8.A team rounds each of 8 equal track sections from 12.46 m to 12.5 m, then adds the rounded values. Compare this total with the total calculated from the unrounded measurements. How much rounding difference is there?

9.The total for the 8 track sections is calculated as 8 × 12.46 m. Which method is more reliable, and why: (A) round 12.46 m first and then multiply, or (B) multiply first and round the final total?

10.A measurement of 6.25 is rounded to 1 decimal place. State the rounded value and explain the rule used for a final digit of 5.

11.A reporter writes, “Rounding 1,248 people to 1,200 creates an error of 48 people, so it is a 48% error.” Identify the mistake and calculate the percentage error to 2 decimal places.