Changing Fractions to Decimals

Fractions can be written as decimals that either terminate (stop) or recur (repeat).

Remember a fraction can be written as $\displaystyle{\frac{a}{b}}$ where $a$ and $b$ are integers and $b\ne 0$.

The decimal form of fractions can be found by dividing the numerator (top) by the denominator (bottom). For the general case above this would be $a\div b$.

Examples

\begin{align*} \frac12 &= 1\div 2 \\[1ex] &=0.5\end{align*}
$\displaystyle{ -\frac{3}{11}=-0.27272727272727\dots}$ the pattern continues forever. From the previous section on decimals we know we can also write this decimal as $-0.\dot{2}\dot{7}$.

If you use your calculator to find out what $-3\div 11$ is it will give you something like $- 0.2727272727$. This is just an approximation of the exact value. A computer will also calculate an approximation.

Write the following fractions in decimal form. For repeating decimals write the first three places after the decimal point followed by three dots (eg $0.\dot{1}$ would be written as $0.111\dots$).

$\displaystyle{\frac34}$		✅ ❌
$\displaystyle{\frac{3}{10}}$		✅ ❌
$\displaystyle{\frac13}$		✅ ❌
$\displaystyle{\frac25}$		✅ ❌
$\displaystyle{\frac29}$		✅ ❌

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