Convert fractions with denominators of 10, 100, or 1,000 into decimals

A fraction with a denominator of 10, 100, or 1,000 represents tenths, hundredths, or thousandths, so its numerator determines the digits in the corresponding decimal places. The relationship between equivalent fractions—such as $3/10=30/100=300/1{,}000$ —explains place-value zeros and conversions such as $7/100=0.07$ , including values greater than one when applicable. This scope excludes arbitrary denominators and repeating-decimal expansions.

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

The denominator tells you the place value:

$10$ means tenths: one digit after the decimal point.
$100$ means hundredths: two digits after the decimal point.
$1{,}000$ means thousandths: three digits after the decimal point.

The numerator tells you how many of those parts you have.

Example: Convert $\frac{7}{100}$ to a decimal

The denominator is $100$ , so the fraction represents hundredths.
Hundredths are written with two digits after the decimal point.
The numerator is $7$ , so write $7$ in the hundredths place.
Use a zero in the tenths place to hold the place:

\frac{7}{100}=0.07

So, $\frac{7}{100}$ is seven hundredths, or $\boxed{0.07}$ .

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

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Fraction to Decimals - Powers of Ten

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