Converting a fraction to a decimal is simple. If you don’t want to do it by hand, you can accomplish it with long division or even your calculator. You’ll be able to easily switch between fractions and decimals once you’ve mastered this technique. Furthermore, once mastered you will be able to take this a step further and convert a decimal to percentages. Keep reading to discover the ins and outs of fractions and decimals.
What is a faction and a decimal?
A Fraction
Fractions are represented as a numerical value in mathematics and can be defined as pieces of a whole. A fraction is a piece or section of a whole that can be any number, a specified value, or an item.
There is a numerator and a denominator in every fraction:
- The denominator shows how many parts have been divided into the whole. It is positioned at the bottom of the fraction.
- The numerator denotes the number of fractional portions shown. It is the top number.
For example, let us look at the fraction ¼ where 1 is the numerator, and 4 is the denominator. To make a whole number, you need 4 quarters. For example, imagine that you need 4 pizza slices to make a whole pizza. In this scenario, each slice is ¼ of the whole pizza.
A Decimal
A decimal point is a dot that is placed between two integers in a decimal group of numbers. Integers or whole numbers are numbers to the left of the decimal point, whereas decimals are numbers to the right of the decimal point. An example of a decimal is 10.4, this decimal is a number that falls between 10 and 11. It is greater than ten but less than eleven.
After the decimal point, a new world of numbers emerges, in which decimal fractions are used to express the value. Each place digit is ten times greater than the preceding place digit as we move to the left. So we have tenths (1/10) to the right of one’s position, then hundredths (1/100) to the right of tenths, and so on. Let’s look at a few examples to get a better understanding:
- 5.8 means 5 and 8 tenths.
- 5.83 means 5, 8 tenths and 3 hundredths.
- 5.083 means 5, 0 tenths, 8 hundredths and 3 thousandths.
Steps to convert a fraction to a decimal
The division symbol can be used to rewrite the line that separates the numerator and denominator in a fraction. To convert a fraction to a decimal, divide the numerator by the denominator. You can accomplish this with a calculator if necessary. As a result, you’ll have a decimal answer.
For example:
- To convert 4/5 just divide the numerator by the denominator (4 ÷ 5) and you get 0.8
- Equally, 75/100 becomes 0.75 when you divide 75 by 100
- Lastly, 5/10 becomes 0.5 when you divide 5 by 10
Expressing fractions as decimals is simple with a calculator but can become quite tricky if you have to do it yourself. Long division will help you do this.
Long Division
Unfortunately, there is no simple fraction to decimal formula. Long division is the best way to change fractions to decimals.
Let us take a look at the following fraction 3/4. If we divide the numerator by the denominator, this can be expressed as 3 ÷ 4. To calculate this without a calculator, you need to put your brain to the test using long division.
- Step 1: To set up the long division equation, place the denominator outside the division bracket (to the left), and the numerator inside the division bracket (to the right). On the diagram, this is shown in black.
- Step 2: When working with fractions where the numerator (3) is smaller than the denominator (4), your answer will be less than 1. As such, write a 0 above the 3 as shown on the diagram in red.
- Step 3: As we can’t divide 3 by 4, things get a little complex. Once Step 2 is complete, you can carry the 3 over and ignore the decimal point. In other words, the 3.0 can be treated as 30. 7 x 4 = 28 and 28 is the closest whole number to 30 that is divisible by 4. Shown in blue on the diagram, write 7 above the first 0 (tenths), and write 28 beneath the 3.0.
- Step 4: You may be saying, well 28 is not 30. What do we do with the remaining 2? This is carried over to the next 0 (hundredths) which can be treated as 20 (shown on the diagram below in green). 20 is divisible by 4 as 4×5=20. As such, above the second 0 (hundredths), write 5. As 20 is divisible and there is no remainder, the long division process is complete.
If you have a remainder, then keep going until you don’t!
The result is 0.75, and this is what 3/4 is as a decimal.
Examples of converting fractions to decimals
Numbers such as 3/4, 1/2 and 1/5 are fairly common and as such will usually be featured on a fraction to decimal conversion chart. Below are some examples of changing fractions to decimals:
- What is 4/5 as a decimal?
This is an easy way to convert a fraction to a decimal. If you multiply the numerator and denominator by 2, the fraction becomes 8/10. Any fraction where the denominator is 10,100,1000, etc. can easily be divided.
8 ÷ 10 = 0.8
Easy Peasy!
- What is 5/8 as a decimal?
Turning fractions into decimals on a calculator is easy, simply type 5 ÷ 8, and your answer should be 0.625. However, with long division, this is how you would calculate the answer:
0.625
8) 5.000
0
5 0
4 8
20
16
40
0
Just remember step 1, step 2, step 3, and step 4.
- What is 3/16 as a decimal?
Sometimes you will be lucky, and like question 1, transforming the denominator into 10,100,1000… is easy. If you multiply the denominator and numerator by 625, you will get the fraction:
1875/10,000
As 10,000 has 4 decimals (i.e., 4 zeros) then you know the decimal will have 4 decimal places. As such, our answer is 0.1875.
- What is 1/3 as a decimal?
This is trickier than it looks as 1/3 is a recurring decimal meaning it is never ending.
In long division it would look like this:
0.3333333333333
3) 1.000
0
1 0
9
10
9
10
9
As you can see, it just keeps going on and on! Obviously, you can’t write 0.33333333333333333333333, so instead you would simply write 0.333.
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