How to Turn a Fraction Into a Decimal: A Simple Step-by-Step Guide
Knowing how to turn a fraction into a decimal is an important math skill. The good news is that the basic idea is much simpler than it may first seem.
If you remember just one rule, remember this:
Divide the numerator by the denominator.
In other words, take the top number of the fraction and divide it by the bottom number.
For example:
3/4 = 3 ÷ 4 = 0.75
That’s it.
But what happens when the division does not come out evenly? And is there a quicker way to convert fractions such as 1/2, 3/5, or 7/20?
Let’s go through it step by step.
What Is a Fraction?
Before converting a fraction to a decimal, it helps to know what the two numbers mean.
In the fraction 3/4:
- 3 is the numerator, or top number.
- 4 is the denominator, or bottom number.
The fraction bar also means division.
So:
3/4 means 3 ÷ 4.
This is why converting a fraction to a decimal is really a division problem.
How to Turn a Fraction Into a Decimal
The main rule is simple:
Divide the numerator by the denominator.
Let’s look at a few examples.
Example 1: Convert 1/2 to a Decimal
Start with:
1/2
Divide the numerator by the denominator:
1 ÷ 2 = 0.5
So:
1/2 = 0.5
This is one of the most common fraction-to-decimal conversions, so it is worth remembering.
Example 2: Convert 3/4 to a Decimal
Start with:
3/4
Now divide:
3 ÷ 4 = 0.75
Therefore:
3/4 = 0.75
Example 3: Convert 5/8 to a Decimal
Start with:
5/8
Divide 5 by 8:
5 ÷ 8 = 0.625
Therefore:
5/8 = 0.625
The same method works every time. You simply divide the top number by the bottom number.
What If the Numerator Is Smaller Than the Denominator?
This is where some students get confused.
For a fraction such as 3/5, the numerator is smaller than the denominator. That simply means the answer will be less than 1.
Convert 3/5:
3 ÷ 5 = 0.6
So:
3/5 = 0.6
You can also think about it this way:
3/5 means 3 parts out of 5 equal parts.
As a decimal, that amount is 0.6.
Using Long Division to Convert a Fraction
You can use long division when the fraction does not convert immediately.
Let’s convert:
3/8
Write the problem as:
3 ÷ 8
Since 8 cannot go into 3, add a decimal point and zeros:
3.000 ÷ 8
Now divide:
8 goes into 30 three times.
3 × 8 = 24
30 – 24 = 6
Bring down the next zero:
60
8 goes into 60 seven times.
7 × 8 = 56
60 – 56 = 4
Bring down the next zero:
40
8 goes into 40 five times.
5 × 8 = 40
The remainder is 0.
So:
3/8 = 0.375
Adding zeros after a whole number does not change its value. For example, 3 is the same as 3.0 or 3.00. This lets you continue the division when necessary.
A Faster Method: Make the Denominator 10, 100, or 1,000
Sometimes you don’t need long division.
If you can change the denominator to 10, 100, or 1,000, you can often convert the fraction very quickly.
For example:
Convert 1/5 to a Decimal
We know that 5 can be multiplied by 2 to make 10.
So multiply both numbers by 2:
1/5 = 2/10
Now 2/10 is easy to write as a decimal:
2/10 = 0.2
Therefore:
1/5 = 0.2
Convert 3/5 to a Decimal
Multiply the numerator and denominator by 2:
3/5 = 6/10
So:
3/5 = 0.6
Convert 7/20 to a Decimal
We can multiply 20 by 5 to get 100.
So:
7/20 = 35/100
Therefore:
7/20 = 0.35
This shortcut works particularly well with fractions whose denominators can easily be changed to 10, 100, or 1,000.
Common Fractions and Their Decimal Equivalents
Some fractions appear so often that it is useful to know their decimal equivalents.
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 2/5 | 0.4 |
| 3/5 | 0.6 |
| 4/5 | 0.8 |
| 1/8 | 0.125 |
| 3/8 | 0.375 |
| 5/8 | 0.625 |
| 7/8 | 0.875 |
| 1/10 | 0.1 |
You do not have to memorize every fraction.
The important thing is to understand the method so you can convert a fraction even when you don’t remember the answer.
What Happens When the Decimal Keeps Going?
Not every fraction produces a decimal that ends.
For example:
1/3
Divide 1 by 3:
1 ÷ 3 = 0.333333…
The 3 continues repeating.
So:
1/3 = 0.333…
This is called a repeating decimal.
Another example is:
2/3 = 0.666…
You may see repeating decimals written with dots to show that the digits continue.
The important thing to remember is that you should not keep adding zeros forever and expect the division to eventually end. Some fractions produce repeating decimals.
What Is a Terminating Decimal?
A terminating decimal is a decimal that ends.
For example:
1/4 = 0.25
The decimal stops after two digits.
Other examples include:
1/2 = 0.5
3/4 = 0.75
5/8 = 0.625
A repeating decimal does not end:
1/3 = 0.333…
Both are valid decimal representations of the original fraction.
How to Turn a Mixed Number Into a Decimal
You can also convert a mixed number into a decimal.
For example:
2 1/2
First convert the fraction:
1/2 = 0.5
Then add the whole number:
2 + 0.5 = 2.5
So:
2 1/2 = 2.5
Let’s try another one:
3 3/4
Convert the fraction:
3/4 = 0.75
Then add the whole number:
3 + 0.75 = 3.75
Therefore:
3 3/4 = 3.75
How to Turn an Improper Fraction Into a Decimal
The same basic rule works with improper fractions.
An improper fraction has a numerator that is equal to or greater than the denominator.
For example:
7/4
Divide:
7 ÷ 4 = 1.75
So:
7/4 = 1.75
You can also convert 7/4 into a mixed number first:
7/4 = 1 3/4
Then:
1 + 0.75 = 1.75
Either method gives you the same answer.
Can You Use a Calculator?
Yes.
If you are allowed to use a calculator, simply enter the numerator, press the division button, and enter the denominator.
For example:
5/8
Enter:
5 ÷ 8
The calculator gives:
0.625
But it is still important to understand what the calculator is doing.
It is simply dividing the numerator by the denominator.
That is the main rule behind every fraction-to-decimal conversion.
Common Mistakes When Converting Fractions to Decimals
Here are a few mistakes students commonly make.
Mistake 1: Dividing the Numbers in the Wrong Order
For:
3/4
You need to calculate:
3 ÷ 4
Not:
4 ÷ 3
The numerator goes first.
Mistake 2: Forgetting the Decimal Point
When the numerator is smaller than the denominator, the answer will usually begin with 0.
For example:
3 ÷ 5 = 0.6
Not 6.
Mistake 3: Stopping Too Early
For some fractions, you need to continue the division beyond one decimal place.
For example:
3/8 = 0.375
Stopping at 0.3 would not give the exact answer.
Mistake 4: Assuming Every Decimal Ends
Some fractions produce repeating decimals.
For example:
1/3 = 0.333…
The division does not end.
A Quick Trick to Remember
When you see a fraction and need to turn it into a decimal, ask yourself:
“What does the fraction bar mean?”
It means division.
Then:
Top number ÷ bottom number = decimal
For example:
2/5 → 2 ÷ 5 → 0.4
7/8 → 7 ÷ 8 → 0.875
9/10 → 9 ÷ 10 → 0.9
Once you remember this, converting fractions to decimals becomes much easier.
Try These Yourself
See if you can convert these fractions into decimals:
- 1/2 = _____
- 3/4 = _____
- 2/5 = _____
- 7/10 = _____
- 3/8 = _____
- 1/3 = _____
- 9/20 = _____
- 5/8 = _____
Answers
- 1/2 = 0.5
- 3/4 = 0.75
- 2/5 = 0.4
- 7/10 = 0.7
- 3/8 = 0.375
- 1/3 = 0.333…
- 9/20 = 0.45
- 5/8 = 0.625
Final Rule to Remember
Turning a fraction into a decimal does not have to be complicated.
Just remember:
Fraction → Divide the numerator by the denominator → Decimal
For example:
4/5 → 4 ÷ 5 → 0.8
If the division ends, you have a terminating decimal.
If the digits continue repeating, you have a repeating decimal.
And when the denominator can easily be changed to 10, 100, or 1,000, you can often use an equivalent fraction as a shortcut.
With a little practice, converting fractions to decimals becomes a quick and familiar skill.
Want More Math Practice?
If you’re looking for printable math practice for elementary students, Eshaal Maths also has math worksheets covering important skills such as multiplication, addition, subtraction and long division.
Explore Eshaal Maths Printable Math Resources →
For students who prefer a physical workbook, Eshaal Maths also publishes math practice books on Amazon.
