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

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.

\[1.42 x 10^4 \frac{kg}{m^3}\]

Unit analysis is the same method as dimensional analysis or factor-label methods.