Long division gives us a way of finding decimal expansions for fractions.

For example, to find a decimal expansion for $\frac{9}{8}$, we can divide 9 by 8.

So $\frac{9}{8} = 1.125$.

\(\require{enclose} \begin{array}{r} 1.125 \\[-3pt] 8 \enclose{longdiv}{9.000}\kern-.2ex \\[-3pt] \underline{8{\phantom{.0}}} \phantom{00} \\[-3pt] 1\phantom{.}0\phantom{00} \\[-3pt] \underline{8\phantom{0}}\phantom{0} \\[-3pt] 20\phantom{0} \\[-3pt] \underline{16\phantom{0}} \\[-3pt] \phantom{0} 40 \\[-3pt] \underline{40} \\[-3pt] 0 \\ \end{array}\)

Sometimes it is easier to work with the decimal expansion of a number, and sometimes it is easier to work with its fraction representation. It is important to be able to work with both. For example, consider the following pair of problems:

- Priya earned $x$ dollars doing chores, and Kiran earned $\frac{6}{5}$ as much as Priya. How much did Kiran earn?
- Priya earned $x$ dollars doing chores, and Kiran earned 1.2 times as much as Priya. How much did Kiran earn?

Since $\frac{6}{5}=1.2$, these are both exactly the same problem, and the answer is $\frac{6}{5}x$ or $1.2x$.

When we work with percentages in later lessons, the decimal representation will come in especially handy.