Question

Convert the following measurement
0.0088(g/cm^3)=_____ kg/m^3

Answer 1

0.00088 kg/m³

Step-by-step explanation:

Given:

`\displaystyle{ \frac{8.8 * {10}^( - 3) \: \text{g} }{ \text{cm}^(3) }}`

Let's consider cm³ to m³ first. We know that m³ is 100 cm³. Therefore, cm³ would equal to m³ × 10 negative squared:

`\displaystyle{ \frac{8.8 * {10}^( - 3) \: \text{g} }{ {10}^( - 2) \: \text{m}^(3) }}`

And from the numerator, 1 kg = 10³ grams. Therefore, 1 gram would equal 10 to negative cube kg Hence:

`\displaystyle{ \frac{8.8 * {10}^( - 3) * {10}^( - 3) \: \text{kg} }{ {10}^( - 2) \: \text{m}^(3) }}`

Then evaluate using law of exponent where if same bases multiply each other, we add the exponents:

`\displaystyle{ \frac{8.8 * {10}^( - 3 - 3) \: \text{kg} }{ {10}^( - 2) \: \text{m}^(3) }} \\ \\ \displaystyle{ \frac{8.8 * {10}^( - 6) \: \text{kg} }{ {10}^( - 2) \: \text{m}^(3) }} \\ \\ \displaystyle{ \frac{8.8 * {10}^( - 6 + 2) \: \text{kg} }{ \: \text{m}^(3) }} \\ \\ \displaystyle{ \frac{8.8 * {10}^( - 4) \: \text{kg} }{ \: \text{m}^(3) }}`

And 8.8 × 10^-4 is equal to 0.00088. Therefore, the answer is 0.00088 kg/m³