Converting Fractions To Decimals - Math Is Fun

Convert Fractions to Decimals

The simplest method is to use a calculator

Just divide the top of the fraction by the bottom, and read off the answer!

Example: What's 58 as a decimal ... ?

... get your calculator and type in "5 / 8 ="

The answer should be 0.625

No Calculator? Use Long Division to Decimal Places

Example: here's what long division of 58 looks like:

0.625 8 )5.000 0 5.0 4.8 20 16 40 40 0

In that case we inserted extra zeros and calculated 5.0008 to get 0.625

Read the Long Division to Decimal Places page for more details.

Example: now let's try 13

0.333... 3 )1.000000 0 1.0 0.9 10 9 10 9 10 Hey! It goes forever!

it is called a repeating decimal.

Why does it repeat? Because if a remainder happens again (such as the "1"), then the same steps will repeat, so the decimal digits repeat too.

We often write it with a bar over the repeating part, or with 3 dots after, so we know it goes on (and on!)

Answer: 13 = 0.3 = 0.33...

See Decimal Expansion to learn more

Also try 16, 17, 19 and many more.

Another Method

Another method you may like. Follow these steps:

• Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s
• Step 2: Multiply both top and bottom by that number
• Step 3. Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)

Example: Convert 34 to a Decimal

Step 1: We can multiply 4 by 25 to become 100

Step 2: Multiply top and bottom by 25:

×25
34	=	75100
×25

Step 3: Write down 75 with the decimal point 2 spaces from the right (because 100 has 2 zeros);

Answer = 0.75

Example: Convert 316 to a Decimal

Step 1: We have to multiply 16 by 625 to become 10,000

Step 2: Multiply top and bottom by 625:

×625
316	=	1,87510,000
×625

Step 3: Write down 1875 with the decimal point 4 spaces from the right (because 10,000 has 4 zeros);

Answer = 0.1875

And we can use that method in a surprising way.

Example: Convert 13 to a Decimal

OK, let's have fun with numbers and try for a quick estimate.

Step 1: Since 3 doesn't go into 10 or 100 or 1000 evenly, let's try a close match:

3 × 333 = 999

Step 2: Let's multiply top and bottom by 333:

×333
13	=	333999
×333

Step 3: Now, 999 is nearly 1,000, so we can write down 333 with the decimal point 3 spaces from the right (because 1,000 has 3 zeros):

Answer = 0.333 (accurate to only 3 decimal places!)

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