Convert Between Fractions and Decimals

Converting between fractions and decimals is a fundamental skill for the GED Mathematical Reasoning test. You will need this ability to compare numbers, evaluate expressions, and solve real-world problems. Whether you are changing \(\color{blue}{\frac{3}{4}}\) to \(\color{blue}{0.75}\) or turning \(\color{blue}{0.6}\) into \(\color{blue}{\frac{3}{5}}\), the process is systematic and quick once you know the rules.

What Does It Mean to Convert Between Fractions and Decimals?

A fraction and a decimal are two different ways of writing the same value. For example, \(\color{blue}{\frac{1}{2} = 0.5}\) and \(\color{blue}{\frac{3}{4} = 0.75}\). Converting between them allows you to use whichever form is more convenient for a given problem.

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How to Convert a Fraction to a Decimal

Divide the numerator by the denominator

Every fraction means division. To convert, divide the top number by the bottom number.

• \(\color{blue}{\frac{3}{4}}\): divide \(\color{blue}{3 \div 4 = 0.75}\)
• \(\color{blue}{\frac{5}{8}}\): divide \(\color{blue}{5 \div 8 = 0.625}\)
• \(\color{blue}{\frac{7}{20}}\): divide \(\color{blue}{7 \div 20 = 0.35}\)
• \(\color{blue}{\frac{11}{25}}\): divide \(\color{blue}{11 \div 25 = 0.44}\)

If the division does not terminate, the decimal repeats (see the Repeating Decimals lesson).

How to Convert a Decimal to a Fraction

Use the place value

Write the decimal digits over the appropriate power of 10 (10 for tenths, 100 for hundredths, etc.), then simplify.

• \(\color{blue}{0.6 = \frac{6}{10} = \frac{3}{5}}\)
• \(\color{blue}{0.35 = \frac{35}{100} = \frac{7}{20}}\)
• \(\color{blue}{0.125 = \frac{125}{1000} = \frac{1}{8}}\)
• \(\color{blue}{0.4 = \frac{4}{10} = \frac{2}{5}}\)
• \(\color{blue}{0.75 = \frac{75}{100} = \frac{3}{4}}\)

Step-by-Step Summary

1. Fraction to decimal: Divide \(\color{blue}{\text{ numerator } \div \text{ denominator }}\). Add zeros after the decimal point as needed.
2. Decimal to fraction: Write the digits over the place-value denominator (10, 100, 1000, …).
3. Simplify the fraction using the GCF.
4. Check by converting back: the fraction and decimal should produce the same value.

Watch: Convert Any Fraction to a Decimal (Video Lesson)

Math Antics shows an easy, reliable method for converting any fraction to a decimal using long division:

Convert Between Fractions and Decimals – Worked Examples

Example 1: Convert \(\color{blue}{\frac{3}{8}}\) to a decimal.

Divide: \(\color{blue}{3 \div 8 = 0.375}\). Answer: \(\color{blue}{0.375}\).

Example 2: Convert \(\color{blue}{0.625}\) to a fraction in lowest terms.

Place value: thousandths. \(\color{blue}{0.625 = \frac{625}{1000}}\). \(\color{blue}{\text{ GCF }(625, 1000) = 125}\). Divide: \(\color{blue}{\frac{625}{125} = 5}\), \(\color{blue}{\frac{1000}{125} = 8}\). Answer: \(\color{blue}{\frac{5}{8}}\).

Example 3: Convert \(\color{blue}{\frac{11}{25}}\) to a decimal.

Divide: \(\color{blue}{11 \div 25 = 0.44}\). Answer: \(\color{blue}{0.44}\).

Example 4: Convert \(\color{blue}{0.4}\) to a fraction in lowest terms.

\(\color{blue}{0.4 = \frac{4}{10}}\). \(\color{blue}{\text{ GCF }(4, 10) = 2}\). Simplify: \(\color{blue}{\frac{4}{10} = \frac{2}{5}}\).

More Practice: Converting Fractions to Decimals (Video)

Khan Academy reinforces fraction-to-decimal conversion with additional examples:

Exercises for Converting Fractions and Decimals

Convert each fraction to a decimal and each decimal to a fraction in lowest terms.

1. \(\color{blue}{\frac{7}{8}}\) (fraction to decimal)
2. \(\color{blue}{\frac{3}{5}}\) (fraction to decimal)
3. \(\color{blue}{\frac{9}{20}}\) (fraction to decimal)
4. \(\color{blue}{0.8}\) (decimal to fraction)
5. \(\color{blue}{0.15}\) (decimal to fraction)
6. \(\color{blue}{0.375}\) (decimal to fraction)

Answers

1. \(\color{blue}{7 \div 8 = 0.875}\)
2. \(\color{blue}{3 \div 5 = 0.6}\)
3. \(\color{blue}{9 \div 20 = 0.45}\)
4. \(\color{blue}{0.8 = \frac{8}{10} = \frac{4}{5}}\)
5. \(\color{blue}{0.15 = \frac{15}{100} = \frac{3}{20}}\)
6. \(\color{blue}{0.375 = \frac{375}{1000} = \frac{3}{8}}\)

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Frequently Asked Questions

What if the fraction gives a repeating decimal?

If the denominator (in lowest terms) has a prime factor other than 2 or 5, the decimal repeats. Write the repeating block with a bar over it. For example, \(\color{blue}{\frac{1}{3} = 0.&\#773;3}\).

How do I convert a decimal greater than 1 (like 1.25) to a fraction?

Treat the whole-number part separately: \(\color{blue}{1.25 = 1 + 0.25 = 1 + \frac{1}{4} = 1 \frac{1}{4}}\), which as an improper fraction is \(\color{blue}{\frac{5}{4}}\).

Why do I need to convert between fractions and decimals on the GED?

Many GED problems require comparing or combining values given in mixed forms. For example, comparing \(\color{blue}{\frac{3}{5}}\) and \(\color{blue}{0.65}\) is easiest if you convert \(\color{blue}{\frac{3}{5} = 0.60}\) first, then compare.

Related Topics

• Repeating Decimals
• Simplifying Fractions
• Convert Between Decimals and Mixed Numbers
• Order of Decimals Mixed Numbers and Fractions
• Convert Between Improper Fractions and Mixed Numbers