Fractions, Decimals, and Percents Study Guide for the Math Basics

Fraction/Decimal/Percent Conversion

Decimals \(\leftrightarrow\) Percents.

Switching between decimals and percents is as simple as moving the decimal place two places. Decimal to percent: move right. Percent to decimal: move left. Examples:

\[0.25 = 25\%\] \[0.333…=33.333…\%\] \[12.4=1240\%\]

Fractions \(\rightarrow\) Decimals.

Any fraction can be written in decimal notation, sometimes as a never ending repeating decimal. One way to convert a fraction to a decimal is to find an equivalent fraction with a power of 10 in the denominator. For example:

\[\frac{1}{2} = \frac{5}{10} = 0.5\]

Otherwise, you’ll just have to do long division.

\[\frac{7}{8} = 7 \div 8 = 0.875\] \[\require{enclose} \begin{array}{r} 0.875 \\ 8 \enclose{longdiv}{7.000} \\[-3pt] \underline{-64}\phantom{00} \\[-3pt] 60\phantom{0} \\[-3pt] \underline{-56}\phantom{0} \\[-3pt] 40 \\ \underline{-40} \\[-3pt] 0 \end{array}\]

Decimals \(\rightarrow\) Fractions.

To write a decimal as a fraction, simply read it, write it, and then simplify. Example: 1.24 is read “one and twenty-four hundredths” which is written \(1 \frac{24}{100}\) and simplifies to \(1 \frac{6}{25}\)

Common Fractions/Decimals/Percents.

Here are some common fractions and their decimal (and percent) equivalents:

\[\begin{array}{|c|c|c|} \hline \textbf{Fraction} & \textbf{Decimal} &\textbf{Percent} \\ \hline \dfrac{1}{5} & 0.2 & 20\% \\ \hline \dfrac{1}{4} & 0.25 & 25\% \\ \hline \dfrac{1}{3} & 0.333... & 33.33…\% \\ \hline \dfrac{2}{5} & 0.4 & 40\% \\ \hline \dfrac{1}{2} & 0.5 & 50\% \\ \hline \dfrac{3}{5} & 0.6 & 60\% \\ \hline \dfrac{2}{3} & 0.666... & 66.66…\% \\ \hline \dfrac{3}{4} & 0.75 & 75\% \\ \hline \dfrac{4}{5} & 0.8 & 80\% \\ \hline \end{array}\]

Putting Numbers in Order

A common question on many tests requires you to put numbers in order when some are whole, decimals, or fractions. For these questions, we suggest you turn them all into decimals first. Then compare them. Try it with these numbers:

\[3.15,\;\;3 \frac{1}{4},\;\; 3,\; \;3 \frac {1}{8}\]

The first three are simple: 3.15, 3, and 3.25 (remember \(\frac{1}{4} = 0.25\)). You’ll need to do some long division to turn \(\frac{1}{8}\) into a decimal.

\[\require{enclose} \begin{array}{r} 0.125 \\ 8 \enclose{longdiv}{1.000} \\[-3pt] \underline{-8}\phantom{00} \\[-3pt] 20\phantom{0} \\[-3pt] \underline{-16}\phantom{0} \\[-3pt] 40 \\ \underline{-40} \\[-3pt] 0 \end{array}\]

So we have

\[3.15,\;\;3, \;\;3.25, \;\; 3.125\]

In order:

\[3,\;\; 3.125, \;\;3.15,\;\; 3.25\]

Now switch back to the original numbers:

\[3, \;\;3 \frac{1}{8}, \;\;3.15, \;\;3 \frac{1}{4}\]