Question

How would you express the value of 14.2 *grams per cubic centimeters* in *kilograms per cubic meter*? Find the answer by using the *unit analysis* method.

Accepted Answer

First, write the value to be converted with its units written as fractions. 

$$14.2 \frac{grams}{cm^3}$$

Multiply with the conversion factors, in such a way that similar units are written in diagonals (for cancelling later): 

$$14.2 \frac{grams}{cm^3} \cdot \frac{(100\;cm)^3}{(1\;m)^3} \cdot \frac{1\;kg}{1000\;g}$$ 

The units in diagonals (1 a numerator, and the other a denominator) will cancel out, such as *gram* and *centimeter*, leaving the desired units of *kilogram* and *meter*.

$$1.42 x 10^4 \frac{kg}{m^3}$$

Flashcard 13 - Upper Level: Mathematics Achievement Flashcard Set for the ISEE

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