Fractions to Decimals

Convert Fractions to Decimals

When we convert fractions to decimals, we divide the numerator by the denominator. In the case that the denominator is a multiple of 10 or can be easily converted to a multiple of 10, we can use a shortcut for the division.

The following diagrams show how to convert from a fraction to a decimal using a shortcut method. Scroll down the page for more examples and solutions.

 

Decimal & Fraction Worksheets
Practice your skills with the following worksheets:
Fraction Worksheets
Decimal Worksheets

1. Denominator is a multiple of 10

The Shortcut Method:

1. The numerator of the fraction will be the digits in your decimal.
2. Count the number of zeros in the denominator (10, 100, 1000, etc.). This number tells you how many decimal places there will be in your decimal.
3. Starting from the right of the numerator, move the decimal point to the left by the number of zeros you counted in step 2. You may need to add leading zeros if the numerator has fewer digits than the number of decimal places required.

Example: \(\frac{7}{10}\)
Numerator: 7
Denominator: 10 (1 zero)
Start with 7, move the decimal one place to the left: 0.7
So, \(\frac{7}{10}\) = 0.7

Example: \(\frac{43}{100}\)
Numerator: 43
Denominator: 100 (2 zeros)
Start with 43, move the decimal two places to the left: 0.43
So, \(\frac{43}{100}\) = 0.43

Example: \(\frac{9}{10000}\)
Numerator: 9
Denominator: 10000 (4 zeros)
Start with 9. We need four decimal places, so add three leading zeros: 0.0009
So, \(\frac{9}{10000}\) = 0.0009

2. Denominator can be easily converted to be a power of 10

If you can transform your fraction into an equivalent fraction where the denominator is 10, 100, or 1000 (etc.), then you can use the above shortcut method to convert the fraction to a decimal.

Example: \(\frac{3}{5}\)
Denominator: 5
We can easily turn 5 into 10 (by multiplying by 2).
Multiply both numerator and denominator by 2.
\(\frac{3×2}{5×2}=\frac{6}{10}\)
So, \(\frac{3}{5}=\frac{6}{10}\) = 0.6

Example: \(\frac{7}{25}\)
Denominator: 25
We can easily turn 25 into 100 (by multiplying by 4).
Multiply both numerator and denominator by 4.
\(\frac{7×4}{25×4}=\frac{28}{100}\)
So, \(\frac{7}{25}=\frac{28}{100}\) = 0.28

Example: \(4\frac{1}{2}\)
Keep the whole number (4) aside for now.
Convert the fraction part, \(\frac{1}{2}\)
Denominator: 2
We can easily turn 2 into 10 (by multiplying by 5).
Multiply both numerator and denominator by 5.
\(\frac{1×5}{2×5}=\frac{5}{10}\) = 0.5
Add the whole number back: 4 + 0.5 = 4.5

When this method is not ideal:
This method is good for fractions with denominators that are factors of powers of 10. However, if the denominator has prime factors other than 2 or 5 (e.g., 3, 7, 11, 13), you won’t be able to turn it into a power of 10 easily. In those cases, direct division (numerator ÷ denominator) is the only way, and you’ll typically get a repeating decimal.

Check out the lesson on Converting fractions to decimals by division

Changing Fractions to Decimals (Denominators that are Multiples of 10)

• Show Video

Writing Tenths and Hundredths with Decimals
This video shows how pictures of tenths and hundreds are connected to both fractions and decimals

• Show Step-by-step Solutions

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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