Festival organisers estimate that \(2.4 \times 10^{5}\) people attended a three-day festival, and that \(3 \times 10^{-2}\) of these bought a printed progra...
Question 1 Report
Festival organisers estimate that \(2.4 \times 10^{5}\) people attended a three-day festival, and that \(3 \times 10^{-2}\) of these bought a printed programme.
- Work out the number of people who bought a programme. Give your answer in standard form. (2)
- Each programme made a profit of \(\pounds 8\). Work out the total profit from programme sales, giving your answer in standard form. (2)
Answer Details
(a) The number of programme buyers is the fraction \(3\times10^{-2}\) of the \(2.4\times10^{5}\) attendees. Multiplying the decimal parts and the powers of \(10\) separately: \(2.4\times3=7.2\), and \(10^{5}\times10^{-2}=10^{3}\), giving \(7.2\times10^{3}\) people. [2 marks]
(b) Multiplying this number of buyers by the \(\pounds8\) profit per programme, again combining the decimal and the power of \(10\) separately: \(7.2\times8=57.6\), and this is \(57.6\times10^{3}\), which in standard form (with the coefficient between \(1\) and \(10\)) is \(5.76\times10^{4}\). [2 marks]
Working in standard form throughout, rather than converting to full decimal numbers, keeps both very large and very small quantities, like \(2.4\times10^{5}\) people and \(3\times10^{-2}\) as a fraction, manageable in the same calculation.
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