A fraction is a division, and decimals are tenths, hundredths and thousandths. So a fraction and a decimal can be two names for the same number.
Key idea
To write a fraction as a decimal, rename it with a denominator of 10, 100 or 1,000, or divide the numerator by the denominator. To write a decimal as a fraction, read it: $0.25$ is 25 hundredths, $\frac{25}{100} = \frac{1}{4}$.
Why it works
$\frac{1}{4}$ of a hundred grid is 25 of its 100 squares, so $\frac{1}{4} = \frac{25}{100} = 0.25$. Multiplying the top and bottom by 25 does not change the amount; it only cuts the pieces into hundredths. Dividing works too: $1 \div 4 = 0.25$.
Worked examples
Worked example: Fourths
Write $\frac{3}{4}$ as a decimal.
- $4 \times 25 = 100$, so multiply the top and bottom by 25.
- $\frac{3}{4} = \frac{75}{100}$, which is 75 hundredths.
Answer: $0.75$
Worked example: Eighths
Write $\frac{3}{8}$ as a decimal.
- $8 \times 125 = 1{,}000$.
- $\frac{3}{8} = \frac{375}{1000}$, which is 375 thousandths.
Answer: $0.375$
Worked example: Decimal to fraction
Write $0.6$ as a fraction in simplest form.
- $0.6$ is 6 tenths: $\frac{6}{10}$.
- Divide the top and bottom by 2: $\frac{3}{5}$.
Answer: $\frac{3}{5}$
Common mistake
Reading the digits straight across, so $\frac{1}{4}$ becomes $0.4$ or $0.14$. But $0.4$ is 4 tenths, more than a third. Check by rounding to a benchmark: $\frac{1}{4}$ is less than $\frac{1}{2} = 0.5$ and more than 0, and $0.25$ fits.