Question

which of the following is equal to 1 g/cm³ ? multiple choice 10⁴ kg/m³ 10⁶ kg/m³ 10² kg/m³ 10³ kg/m³

Explanation:

Step1: Convert grams to kilograms

We know that \(1\space kg = 1000\space g\), so \(1\space g=\frac{1}{1000}\space kg = 10^{- 3}\space kg\).

Step2: Convert cubic centimeters to cubic meters

We know that \(1\space m=100\space cm\), so \((1\space m)^{3}=(100\space cm)^{3}=1000000\space cm^{3}=10^{6}\space cm^{3}\), then \(1\space cm^{3}=\frac{1}{10^{6}}\space m^{3}=10^{-6}\space m^{3}\).

Step3: Substitute the conversions into the density unit

We have \(1\space g/cm^{3}=\frac{1\space g}{1\space cm^{3}}\), substitute \(1\space g = 10^{-3}\space kg\) and \(1\space cm^{3}=10^{-6}\space m^{3}\) into it:
\[

$$\begin{align*} 1\space g/cm^{3}&=\frac{10^{-3}\space kg}{10^{-6}\space m^{3}}\\ &=\frac{10^{-3}}{10^{-6}}\space kg/m^{3}\\ &= 10^{-3 + 6}\space kg/m^{3}\\ &=10^{3}\space kg/m^{3} \end{align*}$$

\]

Answer:

\(10^{3}\space kg/m^{3}\) (the option with \(10^{3}\space kg/m^{3}\))