Fraction to decimal

Here you will learn about converting fractions to decimals using division and using a calculator.

Students will first learn about converting fractions to decimals as part of number and operations fractions in 4th grade. They expand their knowledge of converting fractions to decimals as part of the number system in 7th grade.

What is converting fractions to decimals?

Converting fractions to decimals is representing a fraction as a decimal without changing its value.

For example,

\cfrac{1}{4}=0.25

\cfrac{1}{8}=0.125

\cfrac{2}{7}=0.2857142857…

3 \cfrac{1}{5}=3.2

What is converting fractions to decimals?

Common Core State Standards

How does this relate to 7th grade math?

• 7th grade – The Number System (7.NS.2d)
  Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0 s or eventually repeats.

How to convert fractions to decimals

In order to convert from a fraction to a decimal:

1. Ensure the fraction is written with just a numerator and a denominator. If needed convert the mixed number to an improper fraction.
2. Divide the numerator by the denominator.
3. State the answer clearly in the form ‘fraction’=’decimal.’

Converting fractions to decimals examples

Example 1: converting a simple fraction to a decimal

Convert \cfrac{1}{2} to a decimal.

1. If needed convert the mixed number to an improper fraction.

There is no need to convert as the fraction is already in the correct form.

2Divide the numerator by the denominator.

1 \div 2 \quad You can use long division here.

3State the answer clearly in the form ‘fraction’=’decimal.’

\cfrac{1}{2} = 0.5

Example 2: converting a fraction to a decimal

Convert \cfrac{3}{8} \, to a decimal.

Divide the numerator by the denominator.

3 \div 8

Example 3: converting an improper fraction to a decimal

Convert \cfrac{7}{5} \, to a decimal.

Divide the numerator by the denominator.

7 \div 5

Example 4: converting a mixed number to a decimal

Convert 3 \cfrac{1}{4} \, to a decimal.

Divide the numerator by the denominator.

13\div{4}

Example 5: converting a fraction to a decimal involving a repeating decimal

Convert \cfrac{2}{9} \, to a decimal.

Divide the numerator by the denominator.

2 \div 9

You will notice here that the 2 is repeated and will continue to be repeated. This is therefore a recurring, or repeating decimal and can be shown in the form.

0.\overline{2}

Example 6: converting a mixed number to a decimal involving a repeating decimal

Convert 2\cfrac{1}{7} \, to a decimal.

Divide the numerator by the denominator.

15 \div 7 \quad You can use long division here.

You will notice here that the numbers 1 \, 4 \, 2 \, 8 \, 5 \, 7 after the decimal place are repeated and will continue to be repeated.

This is therefore a repeating decimal and can be shown in the form 0.\overline{142857}, so the whole decimal can be shown as 2.\overline{142857}

Calculator skills

You can perform a fraction to decimal conversion on a calculator by dividing the numerator by the denominator as a simple division equation. Another way is by inputting the fraction into your calculator and then pressing the [s ⇔ d] button.

For example, convert \cfrac{5}{4} to a decimal.

Press the fraction button on the left side of your calculator.

Input the numbers and press the = button.

Press the [ s ⇔ d ] button to have it shown as a decimal.

Therefore, \cfrac{5}{4}=1.25

See also: Calculator skills

Teaching tips for fractions to decimals

• Students will need to have a strong foundation in division and specifically the standard algorithm of division, or long division. Students should also understand the terms dividend and divisor. Review if needed before starting this topic.

• Begin with fractions that convert to simple decimal numbers ending in the tenths, hundredths, or thousandths place. Then move on to fractions that convert to more complex terminating decimals before moving onto fractions that convert to repeating decimals.

• Once students have mastered the calculations, move on to higher-level worksheets that provide them with word problems to provide a real-world context to the topic, which will deepen their understanding. For example, give students a division problem that requires them to use fraction to decimal conversion to calculate a percentage.

Easy mistakes to make

• Incorrectly converting between a mixed number and an improper fraction
  Not correctly converting between numbers in different forms. For example, mixed numbers and improper fractions or forgetting to convert to an improper fraction and using the fractional part of a mixed number only.

• Making mistakes when dividing
  Incorrectly using the standard algorithm of division (or long division).

• Flipping the division order
  Incorrectly dividing the denominator (bottom number) by the numerator (top number), not the other way around.
  For example, \cfrac{5}{7} \, means 5 \div 7 not 7 \div 5.

Related lessons on converting fractions, decimals, and percentages

• Percent to decimal
• Percent to fraction
• Decimal to percent
• Decimal to fraction
• Fraction to percent
• Repeating decimal to fraction

The next lessons are

• Percent
• Compound measures
• Arithmetic
• Properties of equality
• Addition and subtraction

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