How To Convert a Fraction Into a Decimal

Converting Fractions into Decimals Have you ever wondered how to convert a fraction into a decimal? It can be pretty tricky to do so. First of all, let’s go over How To Convert a Fraction Into a Decimal.

What is a Fraction?

Fractions represent equal parts of a whole or a collection. A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken.  The number below the line is called the denominator.  It shows the total divisible number of equal parts the whole into or the total number of equal parts which are there in a collection.

There are different types of fractions. Fractions with numerator 1 are called unit fractions. Fractions in which the numerator is less than the denominator are called proper fractions. Fractions in which the numerator is more than or equal to the denominator are called improper fractions. Mixed fractions consist of a whole number along with a proper fraction.

What is a Decimal?

In algebra, decimals are a set of numbers written together with a dot in between them that is called a decimal point. The numbers to the left of the decimal point are the integers or whole numbers and the numbers to the right of the decimal point are called decimal numbers. In the case of decimals, for the whole number part, the place value system is the same as the whole number. But after the decimal point, there is a different world of numbers going on in which we use decimal fractions to represent the value. When we are going towards the left, each place is ten times greater than the previous place digit.

There are two ways to read a decimal number. The first way is to simply read the whole number followed by “point”, then to read the digits in the fractional part separately. It is a more casual way to read decimals. For example, we read 34.56 as thirty-four point fifty-six. The second way is to read the whole number part followed by “and”, then to read the fractional part in the same way as we read whole numbers but followed by the place value of the last digit. For example, we read 34.56 as thirty-four and fifty-six hundredths.

Converting Fractions to Decimals

The easiest way to convert a fraction to a decimal is just to use your calculator. The line between the numerator and denominator acts as a division line, so 7/29 equals 7 divided by 29 or .241.

If you don’t have access to a calculator though, you can still convert fractions to decimals by using long division or getting the denominator to equal a multiple of 10. We explain both these methods in this section.

Long Division Method

Convert 5/8 to a decimal.

Here is what 5/8 looks like worked out with long division.

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

5/8 converted to a decimal is 0.625

Denominator as a Value of 10 Method

Convert 3/8 to a decimal.

Step 1

We want the denominator, in this case 8, to equal a value of 10. We can do this by multiplying the fraction by 125, giving us 375/1000.

Step 2

Next we want to get the denominator to equal 1 so we can get rid of the fraction. We’ll do this by dividing each part of the fraction by 1000, which means moving the decimal over three places to the left.

This gives us .375/1 or just .375, which is our answer.

Note that this method only works for a fraction with a denominator that can easily be multiplied to be a value of 10. However, there is a trick you can use to estimate the value of fractions you can’t convert using this method. Check out the example below.

Example

Convert ⅔ to a decimal.

There is no number you can multiply 3 by to make it an exact multiple of 10, but you can get close.

By multiplying ⅔ by 333/333, we get 666/999.

999 is very close to 1000, so let’s act like it actually is 1000, divide each part of the fraction by 1000, and move the decimal place of 666 three places to the left, giving us .666

The exact decimal conversion of ⅔ is the repeating decimal .6666667, but .666 gets us very close.

So whenever you have a fraction whose denominator can’t easily be multiplied to a value of 10 (this will happen to all fractions that convert to repeating decimals), just get the denominator as close to a multiple of 10 as possible for a close estimate.

Another Method

Yet another method you may like is to 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)

Examples

Convert 3/4 to a Decimal.

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

Step 2: Multiply top and bottom by 25:

3/4 * 25/25 = 75/100

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

Answer = 0.75

Convert 3/16 to a Decimal.

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

Step 2: Multiply top and bottom by 625:

3/16 * 625/625 = 1875/10000

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

Answer = 0.1875

Convert 1/3 to a Decimal.

Step 1: There is no way to multiply 3 to become 10 or 100 or any “1 followed by 0s”, but we can calculate an approximate decimal by choosing to multiply by, say, 333.

Step 2: Multiply top and bottom by 333:

1/3 * 333/333 = 333/999

Step 3: Now, 999 is nearly 1,000, so let us 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 !!)

Common Decimal to Fraction Conversions

Below is a chart with common decimal to fraction conversions and vice-versa. You don’t need to memorize these, but knowing at least some of them off the top of your head will make it easy to do some common conversions. If you’re trying to convert a decimal or fraction and don’t have a calculator, you can also see which value in this chart the number is closest to so you can make an educated estimate of the conversion.

Conclusion

Fractions and decimals are two types of numbers that belong to different systems. They’re used for measurements, answers to problems and also mathematical, scientific and everyday calculations. So if you know how to convert fractions to decimals or decimals into fractions, then you’ll definitely get a lot of new ways to solve maths problems easier and faster.