Convert fractions with denominators 10, 100, or 1,000 to decimals

A fraction with denominator 10, 100, or 1,000 represents tenths, hundredths, or thousandths and can be written as a terminating decimal by placing the numerator’s digits in the corresponding decimal places, including necessary zeros (for example, $3/10=0.3$ and $3/100=0.03$ ). This connects fraction equivalence, base-ten place value, and decimal magnitude; it does not include converting fractions with other denominators or representing repeating decimals.

Detailed Explanation: Convert fractions with denominators 10, 100, or 1,000 to decimals

The denominator tells you how many digits belong after the decimal point:

Denominator $(10)$ : 1 decimal place (tenths)
Denominator $(100)$ : 2 decimal places (hundredths)
Denominator $(1{,}000)$ : 3 decimal places (thousandths)

Example: Convert $\frac{7}{1{,}000}$ to a decimal.

The denominator is $(1{,}000)$ , so the decimal must have three digits after the decimal point.
Write the numerator, $7$ , in the thousandths place. Add zeros before it so there are three decimal digits:

\frac{7}{1{,}000}=0.007

Therefore, $\frac{7}{1{,}000}$ is seven thousandths, or $\boxed{0.007}$ .

The zeros are necessary because $(0.007)$ has three decimal places, while $(0.07)$ has only two.

Learn by doing: Convert fractions with denominators 10, 100, or 1,000 to decimals

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Fraction to Decimals - Powers of Ten

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