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.

$\color{red}{0.275}$ 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).

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