How to Convert a Decimal to a Fraction

Knowing how to convert a decimal to a fraction is a handy skill. It’s not only useful on math tests, but also in real-life situations where you want to do a part to whole comparison. Multiplying fractions is also arguably simpler than multiplying decimals. In this post, we’ll break this skill down into steps so that you can quickly do these conversions whenever you encounter them, whether it’s real life or on a test.
How to Convert a Decimal to a Fraction
Though the concept might seem difficult at first, converting a decimal to a fraction can be done in just a few simple steps.
First, you need to confirm that the decimal you’re working with is a terminating one. This means it has a finite number of digits rather than a sequence of repeating digits that continue infinitely. Some examples of terminating decimals are:
Once you know that a decimal is terminating, follow the steps below to convert it to a fraction.
How to Convert a Terminating Decimal to a Fraction
Step 1: Create a fraction by putting the decimal over 1.
Write the decimal as a fraction, with the decimal as the numerator and
Step 2: Multiply by the right power of 10 to get rid of the fraction.
Next you’ll need to get rid of the decimal in the fraction you just created. You can’t simply erase it, though, You’ll first need to account for place value. If you know your place value, you know that the decimal
If you don’t know your place values, though, no need to worry; there’s a simple trick to help you out. Simply count the number of digits to the right of the decimal. In the example above there are two. So, you’ll need to multiply both sides of the fraction by
As you can see in the example above, the decimal
Step 3: Reduce the fraction using common factors.
Your last step is reducing the fraction. To do this you need to find common factors of both the numerator and the denominator, and divide each by them again and again until you cannot reduce the numbers any further.
In the example above, both
Because
Let’s look at a simple example. To convert the common decimal
Example 1:
Step 1:
Step 2:
Step 3:
So, we now know that:
Let’s take a look at another, more complicated example. Let’s convert
Example 2:
Step 1:
Step 2:
Step 3:
Because
How to Convert a Non-Terminating, Repeating Decimal to a Fraction
Of course, these examples are only of terminating decimals. Things get a little more complicated when you look at recurring decimals like
In this care, you’ll need to create two algebraic equations to calculate the fraction.
Step 1: Set x equal to the repeating part of the decimal.
For the first equation, let
Step 2: Multiply the equation by the right power of 10 to get one set of the repeating digits to the left of the decimal.
For the second equation, multiply both sides of the equation above by
(Note that if the repeating decimal had more digits, like
Step 3: Solve for x using the two equations.
Use your two equations to solve for
Though converting a decimal to a fraction can sometimes be a complex process, when you break it down into a step by step approach, you’ll keep your work organized and always know what comes next.
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