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More on Changing Decimals to Fractions
Converting decimals, such as 0.275, to fractions involves understanding the base-ten number system. Digits to the right of the decimal point are less than one. They are fractions of one. The position of a digit tells you the power of ten of the denominator of the decimal fraction.
tens | ones | $\bullet$ tenths | hundredths | thousandths |
---|---|---|---|---|
$0$ | $\bullet \;\; 2$ | $7$ | $5$ |
$\color{red}{0.275}$ can be expanded to read:
2 tenths, 7 hunderdths and 5 thousandths.
The column headings show that $0.275$ can be expanded in a number of other ways:
- $2$ tenths, $7$ hundredths and $5$ thousandths
- $275$ thousandths
$$\frac{2}{10} + \frac{7}{100} + \frac{5}{1000}$$
Each fraction can be changed to equal fractions with a denominator of $1000$. \begin{align*} \frac{2}{10} + \frac{7}{100} + \frac{5}{1000}&=\frac{2}{10}\color{red}{\times\frac{100}{100}} + \frac{7}{100}\color{red}{\times\frac{10}{10}} + \frac{5}{1000}\\[1ex] &=\frac{200}{1000} + \frac{70}{1000} + \frac{5}{1000}\\[1ex] &=\frac{275}{1000} \end{align*}
This fraction can now be simplified $\displaystyle{\frac{275}{1000}\color{red}{\div \frac{25}{25}}=\frac{11}{40}}$.
If you did not see that $25$ divides into both $275$ and $1000$, you could divide both numbers by $5$ and then $5$ again:
$\displaystyle{\frac{275}{1000}\color{red}{\div \frac{5}{5}}=\frac{55}{200}}$, but $5$ will still divide into both $55$ and $200$ so repeat.
$\displaystyle{\frac{55}{200}\color{red}{\div \frac{5}{5}}=\frac{11}{40}}$.
Now try these problems. Write the following decimals as fractions in simplest form in the format a/b (for mixed numerals write the integer part in the first box and fraction in the second box).
$0.3$ | ||
$0.8$ | ||
$-0.75$ | ||
$2.05$ | ||
$-0.04$ |
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