Convert terminating decimals to fractions

A terminating decimal represents a fraction whose denominator is a power of 10 determined by the place value of its last nonzero digit: tenths, hundredths, thousandths, and so on. The decimal digits form the numerator, after which the fraction is simplified to an equivalent fraction in lowest terms, recognizing that trailing zeros do not change value; this understanding supports work with rational numbers, percents, and proportional relationships.

Detailed Explanation: Convert terminating decimals to fractions

A terminating decimal can be written as a fraction with a denominator of $10$ , $100$ , $1{,}000$ , and so on. The denominator depends on the place value of the last digit.

Example: Convert $0.375$ to a fraction

Count the decimal places.
The last digit, $5$ , is in the thousandths place, so the denominator is $1{,}000$ .
Write the digits as the numerator.
Ignore the decimal point and use $375$ :

0.375=\frac{375}{1000}

Simplify the fraction.
Both $375$ and $1{,}000$ are divisible by $125$ :

\frac{375\div125}{1000\div125}=\frac{3}{8}

Therefore,

\boxed{0.375=\frac{3}{8}}

Trailing zeros do not change a decimal’s value. For example, $0.5$ , $0.50$ , and $0.500$ all have the same value, but you should use the place value of the last nonzero digit when choosing the denominator.

Learn by doing: Convert terminating decimals to fractions

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Decimals to Fractions - Standard

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