Convert Between Fractions and Decimals

How to convert between fractions and decimals, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

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.̅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