A bus company's fleet of \(480\) buses travels a total of \(4.8\times10^{5}\) km between them in one year, with each bus travelling an equal distance. Work ...
Question 1 Report
A bus company's fleet of \(480\) buses travels a total of \(4.8\times10^{5}\) km between them in one year, with each bus travelling an equal distance. Work out how far one bus travels in the year, giving your answer in standard form. (3)
Answer Details
Sharing a total distance equally among a fleet of buses means dividing the total by the number of buses; carrying out this division using the standard-form value, then re-expressing the result in standard form, keeps the working exact throughout.
Evaluating the total distance: \(4.8\times10^{5}=480\,000\) km. [1 mark]
Dividing by the number of buses: \(480\,000\div480=1000\). [1 mark]
Writing \(1000\) in standard form: \(1000=1\times10^{3}\) km. [1 mark]
The fleet size, \(480\), divides exactly into \(480\,000\) because the digits \(4.8\) in the standard-form total match the fleet size's own leading digits, which is a useful mental check before dividing.
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