Lily is trying to convert $0.003 m^2$ into $mm^2$. Her working is shown as $0.003 m^2 = 0.003 \times 100 \times 10 mm^2 = 3 mm^2$. We are asked to explain the mistake Lily made and to find the correct answer.

1. Problem Description

Lily is trying to convert $0.003 m^2$ into $mm^2$. Her working is shown as $0.003 m^2 = 0.003 \times 100 \times 10 mm^2 = 3 mm^2$. We are asked to explain the mistake Lily made and to find the correct answer.

2. Solution Steps

Lily's mistake is that she multiplied by 100 and 10, which is the conversion factor for meters to millimeters, not square meters to square millimeters.

To convert $m^2$ to $cm^2$, we need to multiply by $100^2 = 10000$.

To convert $cm^2$ to $mm^2$, we need to multiply by $10^2 = 100$.

So to convert $m^2$ to $mm^2$, we multiply by $100^2 \times 10^2 = 10000 \times 100 = 1000000$.

Therefore, we have $0.003 m^2 = 0.003 \times 1000000 mm^2 = 3000 mm^2$.

Lily multiplied by 100 and 10, which is equivalent to multiplying by

1

0

0

0. But she should have multiplied by $100^2 \times 10^2 = 10,000 \times 100 = 1,000,000$.

The correct calculation is $0.003 m^2 = 0.003 \times 1000000 mm^2 = 3000 mm^2$.

3. Final Answer

$3000 mm^2$