Question

express your answer in kilograms per cubic meter.
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5.23 × 10⁻⁶ (kg)/(mm³) = (kg)/(m³)
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Explanation:

Step1: Convert mm³ to m³

We know $1\ \text{mm} = 10^{-3}\ \text{m}$, so $(1\ \text{mm})^3 = (10^{-3}\ \text{m})^3 = 10^{-9}\ \text{m}^3$. This means $\frac{1}{\text{mm}^3} = \frac{1}{10^{-9}\ \text{m}^3} = 10^{9}\ \text{m}^{-3}$.

Step2: Substitute into original value

Multiply the original mass density by the conversion factor:
$5.23 \times 10^{-6}\ \frac{\text{kg}}{\text{mm}^3} = 5.23 \times 10^{-6} \times 10^{9}\ \frac{\text{kg}}{\text{m}^3}$

Step3: Simplify the exponent

Add the exponents of 10: $-6 + 9 = 3$, so $5.23 \times 10^{3}\ \frac{\text{kg}}{\text{m}^3}$

Answer:

$5.23 \times 10^{3}$