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How to Write a Fraction as a Decimal: 2 Simple Methods

how to write a fraction as a decimal: decimal to fraction

If you’re looking for the easiest solution for how to write a fraction as a decimal, we’re here to help. Here, we’ll guide you through three simple ways to convert fractions into decimals.

What Are Fractions?

Fractions have numerators and denominators. Numerators are the top number of a fraction and denominators are the bottom numbers. In the below fraction, 2 is the numerator and 6 is the denominator:

how to write a fraction as a decimal: fraction

Part of writing fractions is simplifying them by finding a common factor, the largest number the numerator and denominator can be divided by. In this case, the common factor is 2. Here’s how the fraction simplifies:

how to write a fraction as a decimal: simplified fraction

Fractions can also demonstrate division problems. In this case, the numerator will be called the dividend, and the denominator will be called the divisor (since it's the value being divided).

If we were to divide the fraction above, the answer would not be a whole number because 1 is smaller than 3. Instead, we would get its decimal form:

how to write a fraction as a decimal: decimal form

Now that we understand how fractions work, let's look at how to determine the decimal equivalent of fractions.

How to Write a Fraction as a Decimal Number

The simplest way to convert fractions into decimals is with a calculator. However, many math problems on tests will not allow you to use calculators. So, you need to know how to find the decimal equivalent of fractions by hand.

Method 1: Long Division

Here’s an example of how to use long division to determine its decimal equivalent. Let’s use the following fraction:

how to write a fraction as a decimal: improper fraction

Let's start by putting this fraction into a long division format. The divisor (6) will be written outside of the right parentheses and the dividend (723) will be placed within the long division symbol:

how to write a fraction as a decimal: long division symbol

We start by determining what value we must multiply 6 by to get the first value of 7. The answer, which is 1, goes above the long division symbol. We’ll subtract the values of 6 x 1, 6, from 7:

how to write a fraction as a decimal: 3rd step of long division

7 minus 6 is 1. Now we will bring the value of 2 from 723 next to the 1. This forms the value of 12. We find the value that 6 needs to be multiplied by equal 12, which is 2:

4th step of long division

Since 6 x 2 is 12, we subtract 12 from 12 and find a remainder of 0.

Now, we will bring down the value of 3 to our bottom line. But since 3 is not divisible by 6, we have to add a 0 above the top 3 followed by a decimal point. Then, we’ll bring down an additional zero. Since 6 multiplied by 5 equals 30, we will then put a .5 at the top:

5th step of long division

Now we know the decimal equivalent of this fraction: 723/6 is 120.5.

decimal equivalent of the fraction

Method 2: Multiply the Denominator

Another way to convert a fraction into a decimal is through multiplication. Here, we’ll find the number you can multiply a denominator by to get 100. Let's use this example to demonstrate:

method 2 multiply the denominator

Because 20 multiplied by 5 equals 100, we need to multiply the numerator 13 by 5 as well:

multiply the numerator

Next, we’ll take the new value of the numerator, 65, and move the decimal point to the left two places to determined its decimal value:

decimal value

How to Write a Fraction as a Decimal Number

There are two methods for writing a fraction as a decimal (well, three if you include using a calculator). You can use long division or find the value the denominator must be multiplied by to get the value of 100.

Once you've mastered these methods, the process of turning a fraction into a decimal value is simple — whether you have a calculator or not.

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