# How to Change a Decimal to a Fraction ••• AndreyPopov/iStock/Getty Images

Changing decimals to fractions may seem difficult at first. Actually, though, changing fractions to decimals requires more work. Changing from decimals to fractions can be done in a few simple steps. Once the process becomes clear, the conversion becomes even simpler.

### Convert Decimal to Fraction

Recognizing place values begins the process to change decimals to fractions. From the decimal point, moving to the right, the place values are tenths, hundredths, thousandths, ten thousandths, hundred thousandths and so on. Notice that these place values end with "th," which differentiates the place values from whole number place values. For example, the decimal 0.2 reads as 2 tenths while the number 2 reads as simply two, or as having a 2 in the ones place.

To convert a decimal to a fraction, determine the place value of the number farthest to the right in the decimal. For example, the decimal 0.125 has the number 5 in the far right position. Naming place values from left to right puts 1 in the tenths place, 2 in the hundredths place and 5 in the thousandths place.

The place value of the far right number becomes the denominator of the fraction. In the example of decimal 0.125, the denominator of the fraction will be 1,000 because the 5 is in the thousandths place.

The decimal number becomes the numerator in the fraction. Because the denominator equals the place value, the decimal disappears in the fraction. In the example, the numerator therefore becomes 125.

Now that the denominator has been determined and the numerator defined, you can write the fraction equivalent of the decimal 0.125. The decimal 0.125 equals the fraction:

\frac{125}{1000}

Since this fraction is not in its simplest form, the fraction will need to be simplified.

The fraction (125/1000) can be simplified. Both the numerator and the denominator are divisible by 5, so a good starting point for simplifying this fraction is

\frac{125}{1000} = \frac{25}{200}

Dividing by the numerator and denominator by 5 again yields

\frac{25}{200} = \frac{5}{40}

Examining the fraction (5/40) shows that both the numerator and denominator can be divided by 5, so dividing again gives

\frac{5}{40} = \frac{1}{8}

The final answer, therefore, in the example problem to change the decimal 0.125 to a fraction is

0.125 = \frac{1}{8}

### Special Case: Repeating Decimals

Sometimes decimals do not terminate but repeat a number or series of numbers. For example, the number 0.959595 . . . repeats the 95 again and again. In this case, the far right number before the repeat lies in the hundredths place. In this case, the denominator will be one less than 100 or 99. The fraction becomes

\frac{95}{99}

### Example Problems

Sample Problem 1:​ Convert the decimal 0.24 to a fraction.

Begin by recognizing that the far right number, 4, is in the hundredths place. Therefore, the denominator of the fraction will be 100, and the numerator will be 24. Evaluating the fraction gives

\frac{24}{100}

Since both 24 and 100 can be divided by 4, simplify using:

\frac{24 ÷ 4}{100 ÷ 4} = \frac{6}{25}

This fraction cannot be simplified further, so the decimal 0.24 equals the fraction (6/25).

Sample Problem 2:​ Convert the repeating decimal 0.6212121 . . . to a fraction.

Begin by recognizing that the last number before the repeat begins, the number 1, lies in the thousandths place. The denominator of the fraction therefore will be

1000-1 = 999

and the numerator will be 621. The fraction becomes

\frac{621}{999}

Both 621 and 999 are divisible by 3 and 9. Therefore, the fraction can be simplified by dividing both by 9, and so the decimal equals the fraction:

0.621 = \frac{621 ÷ 9}{999 ÷ 9} = \frac{69}{111}

### Decimal to Fraction Calculators

Online decimal to fraction calculator websites save time once you achieve competency in the conversion process. These websites perform the calculation quickly. Some calculators show the steps of the procedure while others simply show the answer.

### Decimal to Fraction Tables

Despite the availability of online decimal to fraction calculator programs, decimal to fraction tables provide a useful reference to change decimal to fraction measurements for common dimensions. Tables that show decimal to fraction inches are particularly useful to engineers, machinists and mechanics. These tables may also include metric equivalents.

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