Convert Decimals to Fractions
Decimals and fractions are two ways of showing the same value. Fractions are useful in many cases, such as in recipes and dividing things into parts. Let's explore how we can convert decimals into fractions step by step!
To convert a decimal to a fraction follow these steps:
- Step 1: Write down the decimal divided by 1, like this: decimal 1
- Step 2: Multiply both the top and bottom by 10 for every number after the decimal point.
If there are two digits after the decimal point then multiply by 100 (10 × 10), if there are three digits then multiply by 1000, etc. - Step 3: Simplify (or reduce) the fraction
Example: Convert 0.75 to a fraction
Step 1: Write down 0.75 divided by 1:
0.75 1
Step 2: Multiply both top and bottom by 100 (because there are 2 digits after the decimal point so that is 10×10=100):
| × 100 | ||
 |
||
| 0.75 1 | = | 75 100 |
 |
||
| × 100 | ||
(Do you see how it turns the top number
into a whole number?)
Step 3: Simplify the fraction (this took me two steps):
| ÷5 | ÷ 5 | |||
| |
||||
| 75 100 | = | 15 20 | = | 3 4 |
| |
||||
| ÷5 | ÷ 5 | |||
Answer = 3 4
Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction !
Example: Convert 0.625 to a fraction
Step 1: Write down:
0.625 1
Step 2: multiply both top and bottom by 1,000 (3 digits after the decimal point, so 10×10×10=1,000)
625 1000
Step 3: Simplify the fraction (it took me two steps here):
| ÷ 25 | ÷ 5 | |||
| |
||||
| 625 1000 | = | 25 40 | = | 5 8 |
| |
||||
| ÷ 25 | ÷ 5 | |||
Answer = 5 8
When there is a whole number part, put the whole number aside and bring it back at the end:
Example: Convert 2.35 to a fraction
Put the 2 aside and just work on 0.35
Step 1: Write down:
0.35 1
Step 2: multiply both top and bottom by 100 (2 digits after the decimal point so that is 10×10=100):
35 100
Step 3: Simplify the fraction:
| ÷ 5 | ||
|
||
| 35 100 | = | 7 20 |
|
||
| ÷ 5 | ||
Bring back the 2 (to make a mixed fraction):
Answer = 2 7 20
Example: Convert 0.333 to a fraction
Step 1: Write down:
0.333 1
Step 2: Multiply both top and bottom by 1,000 (3 digits after the decimal point so that is 10×10×10=1,000)
333 1000
Step 3: Simplify Fraction:
Can't get any simpler!
Answer = 333 1000
But a Special Note:
If you really meant 0.333... (in other words 3s repeating forever which is called 3 recurring) then we follow a special method.
Start as usual:
0.333... 1
Then multiply both top and bottom by 3:
| × 3 | ||
|
||
| 0.333... 1 | = | 0.999... 3 |
|
||
| × 3 | ||
And 0.999... = 1 (Does it? - see the 9 Recurring discussion for more if you are interested), so:
Answer = 1 3
As well as 0.333... we can look out for other patterns such as:
Example: Convert 0.444... to a fraction
Step 1: Write down:
0.444... 1
The pattern is similar to 19 = 0.111...
Step 2: Try multiplying both top and bottom by 9:
| × 9 | ||
|
||
| 0.444... 1 | = | 3.999... 9 |
|
||
| × 9 | ||
Step 3: Simplify:
4 9
Conversion Tool
You can also try the Decimal to Fraction Calculator