Converting Decimals and Fractions to Percents

In our last video lesson we learned how to convert a percent to a decimal or a fraction. And to do that it involved dividing by a hundred. Well, in this lesson we're going to do the opposite. We're going to start with a decimal or fraction and convert it to a percent. So that means we have to do the opposite operation. So instead of dividing by 100, you'll see that we'll be multiplying by 100.

Let's look at some examples. First, we'll convert a decimal to a percent. So we'll multiply the decimal by 100 and then place a percent sign after it. So let's convert zero point 47 to a percent. We'll take 100 and multiply it by that decimal. And remember, when we're doing multiplication, we're going to multiply each digit of the second number times the top number and we'll start at the end.

So seven times 100 gives us 700. Four times 100 gives us 400. And we move it over one place value to the left. And then we have the zero that we can multiply by 100, but that would just give us zero. So you don't have to write that step, but you could. And when we add all those together, we get 4700.

Now we need to figure out where the decimal point goes in our answer. So we need to look at the digits that we started with and see how many digits are after a decimal point. Well, 100 doesn't have a decimal point at all, but in the zero point 47, we have two digits after a decimal point. So altogether we have two digits after a decimal point. So our answer needs to have the same.

So if we place the decimal point right between that seven and zero, we do have two digits after our decimal point. And then we just need to place our percent sign. And since we only have zeros after our decimal point, we don't have to include those in our final answer. So we could just write this as 47%. So now we can see that zero point 47 as a percent is 47%.

And next we'll look at converting a fraction to a percent. Our first step is to convert the fraction to a decimal. And then once it's a decimal, we follow the same steps of converting a decimal to a percent. So we'll multiply by 100 and then place a percent sign at the end. So let's convert three-fourths to a percent.

We'll set it up as long division with three divided by four. And since four can't go into three, we'll need to add a decimal point and some zeros after the three. And then we'll line up a decimal point in our quotient. And now four goes into 30 seven times, four times seven gives us 28, subtract. We get two, bring down the other zero, four goes into 20 five times.

Multiply the four times five get 20 and we have no remainder. And it's important that we end up with no remainder. If we did have a remainder here, we would need to add more zeros after the three and keep going until we don't have a remainder left. But we're all finished making this into a decimal. And now we can multiply that decimal zero point 75 times 100, which gives us 75, and then finally put a percent sign at the end.

So three fourths, converted to a percent, is 75%. So remember, when converting a fraction to a percent, it's always easier to convert it to a decimal first and then convert that decimal to a percent.