Convert Decimals to Fractions

Step 1: Write out the decimal divided by 1.

Step 2: Safely remove the decimal point by multiplying both top and bottom by this magical number: a 1 followed by a 0 for every number in the decimal that is right of the decimal point.

Step 3: Reduce (simplify) the fraction

Example 1: Express 0.75 as a fraction

Step 1: write down:

Step 1: multiply both top and bottom by 100 (there were 2 digits after the decimal place so there should be a 1 and 2 zeros)

Step 3: Simplify Fraction:

Answer = 3/4

Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction!

Example 2: Express 0.625 as a fraction

Step 1: write down:

Step 1: multiply both top and bottom by 1,000 (there were 3 digits after the decimal place so there should be 3 zeros)

Step 3: Simplify Fraction:

Answer = 5/8

Example 3: Express 0.333 as a fraction

Step 1: write down:

Step 1: multiply both top and bottom by 1,000 (there were 3 digits after the decimal place so there should be 3 zeros)

Step 3: Simplify Fraction:

Answer = 333/1,000

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 this case we would write down:

Then MULTIPLY both sides by 3:

And 0.999... = 1 (Do you agree? See Our 9 Recurring discussion, so:

Answer = 1/3