Convert Decimals to Fractions

To convert a Decimal to a Fraction follow these steps:

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 (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 (there are 3 digits after the decimal point so that is 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 it 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 (there are 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 (makes 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 (there are 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 need to follow a special argument. In that case we write down:

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