# How to Convert a Decimal to a Fraction: 11 Steps

Converting a decimal to a fraction is not as difficult as it sounds. To do so, follow these steps.

## Steps

### Method 1 of 2: If it is a closed decimal

#### Step 1. Record the decimal

If it is a closed decimal, it should end after one or more places from the decimal point. Let's say you are working with the closed decimal.325. Write it down.

#### Step 2. Convert the decimal to a fraction

This is done by counting the digits after the decimal point. In the number.325 there are three digits after the decimal point. Therefore, you should put the number "325" on top of the number 1000, which is really just the number 1 followed by three zeros. If you were working with the number.3, which only has one digit after the decimal point, then we would represent it as 3/10, that is, the number 3 above the number 1 with a zero added at the end.

### Say the decimal out loud. In this case.325 = "325 thousandths". Sounds like a fraction! Write it down:.325 = 325/1000

#### Step 3. Find the greatest common divisor (GCF) of the numerator and denominator of the fraction you just created

This is done to simplify the fraction. Find the largest number that you can divide both 325 and 1000 by with no remainder. In our case, the GCF of both numbers is 25, because 25 is the largest number that fits a certain number of times in our two numbers without subtracting anything.

• You don't have to find the DCM instantly. Another way to simplify fractions is to do it through trial and error. For example, if the two numbers you are working with are even, divide them by 2 repeatedly until one of them becomes odd or you can no longer divide. If your two numbers are even and odd, try dividing them by 3.
• If the numbers you are working with end in 0 or 5, divide them by 5.

#### Step 4. Divide both numbers by the GCF to simplify the fraction

Divide 325 by 25 to get 13 and divide 1000 by 25 to get 40. The simplified fraction is 13/40. Therefore,.325 = 13/40.

### Method 2 of 2: If it is a repeating decimal

#### Step 1. Record the decimal

A repeating decimal is a decimal that follows an endless number pattern. For example, 2.345454545 is a repeating decimal. Here what we want is to solve the equation for x. Write: x = 2.345454545.

#### Step 2. Multiply the number by a power of ten large enough so that that part of the decimal that does not repeat periodically is to the left of the decimal point

In our example a simple power of 10 will suffice, so write: "10x = 23.45454545…." This is done because if you multiply the part to the right of the equation by 10, then you also have to multiply the part to the left by 10.

#### Step 3. Multiply the equation by another power of 10 to move more digits to the left of the decimal point

In this example, what we will do is multiply the decimal by 1000. Write down: "1000x = 2345.45454545…." This is done because if you multiply the right part of the equation by 1000, then you also have to multiply the left part by 1000.

#### Step 4. Place the variable and constant terms vertically aligned

You must place them like this before proceeding to subtract them. Line up the second equation above the first so that 1000x = 2345.45454545 is on the top and 10x = 23.45454545 is on the bottom, just like you do with subtraction.

#### Step 5. Do the subtraction

Subtract 10x from 1000x to get 990x, and subtract 23.45454545 from 2345.45454545 to get 2322. Now you have 990x = 2322.

#### Step 6. Solve the equation for x

Knowing that 990x = 2322, you can now find "x" by dividing both sides of the equation by 990. So, x = 2322/990.

#### Step 7. Simplify the fraction

Divide the numerator and denominator by any common factors. Find the greatest common divisor of the numerator and denominator to ensure that you have completely simplified. In this example, the GCF of 2322 and 990 is 18, so you can divide both 990 and 2322 by 18 to simplify the numerator and denominator of the fraction. 990/18 = 55 and 2322/18 = 129. Therefore, 2322/990 = 129/55. You're done.