How to Convert Fractions to Decimals

Learning how to convert fractions to decimals can be a challenge for students. Try these tips to explain how those tricky fractions can be switched over to their dotted counterparts.

Fractions vs. Decimals
Everyone is familiar with whole numbers; for example, the numbers 1, 2 and 3 are whole numbers. Whole numbers can also be broken down into parts of a whole, such as a half, a quarter or an eighth. We call those numbers fractions. You're probably familiar with seeing them written out like this: ½, meaning one half. A fraction can also be represented in decimal form. Decimal form doesn't change the value of the number, it's just another way writing it.

Fractions are made up of two parts, the numerator and the denominator. The numerator is the top half of the fraction, while the denominator is the bottom half. So for our ½ example, 1 is the numerator and 2 is the denominator. The line that separates the numerator and denominator is actually a mathematical symbol for division. So what ½ is actually saying is 1 divided by 2. To write this as a decimal, you just need to complete the equation.

Getting Decimals from Fractions
Get a piece of paper and write the symbol for long division. It should look like a vertical line with a "roof" that extends to the right. The numerator of the fraction always goes under the roof. The denominator goes outside. So when you write the formula, it should look like the following: 2/1.

You know that 2 can't go into 1 a whole number of times, so in order to complete the equation, you need to add a decimal place. Draw a dot after the 1; this dot is the decimal. Add a 0 after the decimal. Your equation should now look like this: 2/1.0.

Ignore the decimal for a moment and ask yourself if 2 can go into 10? If so, how many times? The number 10 can be divided by 2 a total of 5 times. Write the number 5 on top of the "roof" over the 0. Take the 5, multiply it times the 2 and write 10 underneath the 1.0. Subtract 10 from 10 and your left with a remainder of 0. Once you reach a remainder of 0, you know that the division is done. Next, carry the decimal point up from the bottom and place it on the
"roof," directly in front of the 5. Place a zero in front of the decimal. Your answer should look like this: 0.5. You just converted the fraction ½ into decimal form.

Let's do one more example using one third, or 1/3. Set up the equation the exact same way as above, using the new numbers. You'll notice that 3 can only go into 10 a total of 3 times, leaving a remainder of 1. Since you want to get a remainder of 0, you'll have to add more decimal places. To do this, add another 0 under the "roof" right next to the first one.

You'll notice that this is a pattern that will continue indefinitely, so we'll use decimal rounding to get an answer. To round to 3 decimal places, you look at the fourth space and see if it's lower than 5. If the answer is yes, you round down and leave the third decimal place alone. If the answer is no, then the third decimal place gets rounded up to the next number.

The answer for 1/3 should look like this in decimal form, rounded to three places: 0.333.

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