Fractions, decimals and percents are different ways of expressing the same value. Here’s how to convert them from one form to another.
Converting decimals to fractions
For any decimal, you should be able to figure what the last place in your decimal is. For example, .125 has digits in the tenths’, hundredths’ and thousandths’ place. Thus, .125 is essentially 125 thousandths which translates to 125/1000.
Converting decimals to percentages
Percent literally means “over 100”. i.e. x% = x/100.
So if you want to find what percent 12.5 is, you are trying to find x in this equation
If you rearrange the equation to isolate x on one side, you’ll see that to find x, you just need to multiply your decimal by 100. Thus, in this case, 12.5 = 1250%
Converting fractions to decimals
Converting any fraction to a decimal involves long division. A fraction is essentially the numerator divided by the denominator. Thus 3/5 is simply 3 divided by 5, which you can work out by long division to be 0.6
Of course the GMAT is not going to use such as fractions, so be sure to know how to do long division!
Converting fractions to percents
As mentioned earlier, x% is x/100 – meaning that it is a fraction with 100 as the denominator. So to find out what percent a fraction is, you need to manipulate the fraction you have to have 100 in the denominator and the numerator will be the percentage.
Suppose we need to convert into its percentage form. You need to convert it to an equivalent fraction with 100 as the denominator and find the numerator.
Thus, you are solving . (Solve this on your own and see if you get 37.5%)
Converting percents to fractions
This one is very easy and you should know by now that x% is x/100. Thus if you wanted to convert 320% to a fraction, it would be which you can simplify to be
Converting percents to decimals
From earlier, we learned that to convert decimals to percents, we multiplied the decimal by 100. To do the reverse (i.e. convert percents to decimals) we do the opposite – divide by 100.
This table summarizes what you need to do when you’re trying to convert something in the left column to a form in the top row.
Now practice fractions, decimals, and percents on Grockit!
