Convert terminating decimals to fractions

A terminating decimal is interpreted through place value as an integer number of tenths, hundredths, thousandths, or other powers of ten, so it can be written as the digits without the decimal point over 10, 100, 1,000, and so on; decimals greater than 1 may produce improper fractions. The resulting fraction is simplified by dividing numerator and denominator by common factors, while preserving equivalence and recognizing that trailing zeros do not change value. Repeating decimals and more advanced rational-number conversions are not included.

Detailed Explanation: Convert terminating decimals to fractions

A terminating decimal ends, or stops, after a certain number of decimal places.

To convert it to a fraction:

Count the digits to the right of the decimal point.
Write the digits without the decimal point as the numerator.
Use a denominator of $10$ , $100$ , $1{,}000$ , and so on, based on the number of decimal places.
Simplify the fraction if possible.

Example: Convert $2.75$ to a fraction.

There are two digits to the right of the decimal point, so the denominator is $100$ :

2.75=\frac{275}{100}

Now simplify by dividing the numerator and denominator by their greatest common factor, $25$ :

\frac{275\div25}{100\div25}=\frac{11}{4}

Therefore,

\boxed{2.75=\frac{11}{4}}

The fraction is improper because $2.75$ is greater than $1$ .

Learn by doing: Convert terminating decimals to fractions

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Decimals to Fractions - Standard

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