A corner shop stocks a supersized gift box of chocolates. The standard box has a mass of \(5^3\) grams, and the supersized box has a mass \(5^2\) times grea...
Question 1 Report
A corner shop stocks a supersized gift box of chocolates. The standard box has a mass of \(5^3\) grams, and the supersized box has a mass \(5^2\) times greater than the standard box.
- Find the mass of the supersized box, giving your answer as a power of 5. (1)
- Work out the mass of the supersized box in grams. (1)
- Work out the mass of the supersized box in kilograms, correct to 2 decimal places. (2)
Answer Details
This question combines the multiplication law of indices with converting a power to a number, then converting units.
(a) The supersized box is \(5^2\) times heavier than the standard \(5^3\) g box, so multiply the powers by adding exponents: \[ 5^3 \times 5^2 = 5^{3+2} = 5^5 \] [1 mark]
(b) Evaluating gives the mass in grams: \[ 5^5 = 3125 \text{ grams} \] [1 mark]
(c) Converting grams to kilograms means dividing by 1000: \[ 3125 \div 1000 = 3.125 \text{ kg} \] which rounds to \(3.13\) kg (2 d.p.) [2 marks]
Rounding to 2 decimal places means looking at the third decimal digit; here it is 5, which rounds the second digit up from 2 to 3.
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