Fractions, Decimals and Percentages

The word percent literally means per hundred. Per — cent, like century, or cents in a dollar. So 50 percent just means 50 out of a hundred. And what is 50 hundredths as a decimal? Zero point five zero. They're the same number.

To go from a decimal to a percentage, all we do is shift the decimal point two places to the right and add a percent sign. Zero point five zero — shift the dot — fifty percent. To go the other way, shift it back two places to the left.

Let's practise. Zero point seven five — shift the dot — seventy-five percent.

Zero point two — shift the dot — twenty percent.

Going backwards: thirty-five percent — shift the dot back — zero point three five. That's all there is to it.

Ordinarily there would be 6 conversions to learn between fractions, decimals and percentages. But we just showed that decimal and percentage are basically the same thing. Just move the dot. So thinking about percentages and decimals as pretty much the same, there are only two real conversions to remember. Fraction to percentage, and percentage to fraction.

Let's turn three quarters into a percentage. Since percent means out of a hundred, we need to write three quarters as something over a hundred. Look at the bottom numbers. What do we multiply four by to get a hundred? Twenty-five. So we multiply the top by twenty-five as well. Three times twenty-five is seventy-five. So three quarters is seventy-five percent.

Here's the calculator method. The fraction line just means divide. So three quarters means three divided by four. Type three, divide, four, equals. The calculator shows zero point seven five. That answer is 3/4 as a decimal. Now shift the decimal two places — seventy-five percent.

Let's try another one. Convert seven twentieths to a percentage. We need to make it out of a hundred. What do we multiply twenty by to get a hundred? Five. Multiply the top by five as well. Seven times five is thirty-five. So seven twentieths is thirty-five percent.

Now with the calculator. Seven twentieths means seven divided by twenty. Seven, divide, twenty, equals — zero point three five. Shift the decimal — thirty-five percent.

To go from percentage to fraction, remember — percent means out of a hundred. So sixty percent is just sixty over a hundred. Now simplify. Both sixty and a hundred divide by twenty. Sixty divided by twenty is three, a hundred divided by twenty is five. So sixty percent is three fifths.

One more: twenty-five percent. Write it as twenty-five over a hundred. Both divide by twenty-five. Twenty-five divided by twenty-five is one, a hundred divided by twenty-five is four. So twenty-five percent is one quarter.

Let’s try a trickier one. Three point five percent. Write it as three point five over a hundred. But we don’t want a decimal in our fraction. We can get rid of it by multiplying top and bottom by ten. Three point five times ten is thirty-five. A hundred times ten is a thousand. Now simplify. Both thirty-five and a thousand divide by five. Thirty-five divided by five is seven. A thousand divided by five is two hundred. So three point five percent equals seven over two hundred.