Lily is trying to convert 0.003m^2 into mm^2 . Her workings are shown below. a) Write a sentence to explain the mistake that Lily has made. b) What answer should Lily have given?

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Lily is trying to convert 0.003m^2 into mm^2 . Her workings are shown below. a) Write a sentence to explain the mistake that Lily has made. b) What answer should Lily have given?

Answer 1

a) Lily made a mistake by not considering that she is dealing with square units. She should have multiplied by \(1,000,000\) (or \(10^6\)), not by 1000 (or \(10^3\)), because there are \(1,000,000\) square millimeters in a square meter. b) The correct answer should be \(3,000 \, \mathrm{mm}^2\).

Answer 2

## Step 1: First, we need to understand the mistake Lily has made. Lily tried to convert \(0.003 \, \mathrm{m}^2\) to \(\mathrm{mm}^2\) by multiplying by 100 and then by 10. This is incorrect because when converting square meters to square millimeters, we should multiply by \(1,000,000\) (or \(10^6\)), not by 1000 (or \(10^3\)). This is because there are \(1,000 \times 1,000 = 1,000,000\) square millimeters in a square meter. ### \(1 \, \mathrm{m}^2 = 1,000,000 \, \mathrm{mm}^2\) ## Step 2: Now, we correct Lily's mistake by multiplying \(0.003 \, \mathrm{m}^2\) by \(1,000,000\) to convert it to \(\mathrm{mm}^2\). ### \(0.003 \, \mathrm{m}^2 \times 1,000,000 = 3,000 \, \mathrm{mm}^2\)

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Lily is trying to convert 0.003m^2 into mm^2 . Her workings are shown below. a) Write a sentence to explain the mistake that Lily has made. b) What answer should Lily have given?

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