Fraction decimal and percent from visual model

So let's assume that this entire square represents a hole, and we can see that part of it is shaded in blue. What we're going to do in this video is try to represent the part that is shaded in blue as a fraction, as a decimal, and as a percent.

So pause the video and see if you can do that.

Well, let's first think about it as a fraction. The whole is split into 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 equal sections, and six of them are filled in. So the blue represents six tenths of a whole, or you could just say six tenths. You could also rewrite that: if you divide the numerator and the denominator by two, that's the same thing as 3 over 5.

Fair enough. Now let's represent it as a decimal. What decimal would it be? Pause the video again and see if you can do that.

Well, 6 tenths, we could literally just go to our place value. So that's the ones place, we have a decimal, and then you have your tenths place. We have six tenths, so you could just put it right over there. We are putting a six in the tenths place to represent six tenths.

Now what about a percentage? Well, percent means per hundred. So, one way to think about it is six over ten is the same thing as what per 100? That is equal to, if we multiply the numerator and the denominator by 10, that's the same thing as 60 per hundred. Or, another way of thinking about it: 60 per, instead of 100, you could say cent. So, this would be equal to—this would be equal to 60 percent.

Let's do another example. So here, once again, our entire square represents a hole. See if you can represent this as the part that's shaded in blue as a fraction. Pause the video and do that.

Well, you can see that this is a 10 by 10 grid, so there's a hundred equal sections here—one hundred equal sections. Each of these squares represents one hundredth. And how many of them are there? Let's see. This row is 10, 20, 30, 40, and then one, two, three, four. So this is 44 over 100: forty-four hundredths.

We could actually represent this in other ways. We could divide the numerator and the denominator by four, in which case you would get 11 over 25. That's another way to represent this same fraction.

Now what about as a decimal? Well, 44 hundredths, you could say, well, you have your ones place, and then this is the same thing. You literally just say this is 44 hundredths. This is another way of representing 44 hundredths. It's four tenths and four hundredths—is 44 hundredths.

And then if you were to do a percent, well, this is 44 per 100 or 44 hundredths. But even here, I like looking at it as 44 per 100 or 44 percent. So this is going to be 44 percent, and we're done.