Sal shows the connection between decimals and fractions using a grid diagram and number lines.
- [Voiceover] We are told the square below represents one whole. So this big square here represents a whole. Express the shaded area as both a fraction and a decimal. So let's see, we've taken the whole and we've divided it into one, two, three, four, five, six, seven, eight, nine, ten, equal sections. Each of these columns or each of these tall rectangles represent one tenth of the whole because they are ten equal sections that it has been split into. So each of these is a tenth and let's see we have filled in one, two, three, four, five, six, of those tenths. So if I wanted to represent it as a fraction I would say this is 6/10 and if I were to represent it as a decimal I would say, okay, well, I have zero ones and I have six tenths, so as a decimal it is 0.6. Let's do a couple more of these examples. So let's say, so okay, look at that. Now I have, let's see, the big square represents one whole. Express the shaded area as both a fraction and a decimal. So what's going on over here? So I have ten rows and in each row I have ten squares. So ten times ten. This has a hundred squares in it. So I've divided my whole into a hundred equal sections. So each of these little squares is one hundredth. So here I have shaded in one, two, three, four, five out of the hundred hundredths, or I could say I have five hundredths right over here. So as a fraction, I could write this as 5/100 and as a decimal I could say, oh, I have no ones. I have no tenths and I have five hundredths. Let's do a couple more examples of this. So let's say that I wanted to... Let's see, it says, express the location of the point on the number line as both a fraction and a decimal. All right. So let's think about it. So this is 2/10, this is 3/10. And you see it is 0/10, 1/10, or this is 0, 1/10, 2/10, 3/10, and before each, or between each tenth they've split it into ten equal sections. One, two, three, four, five, six, seven, eight, nine, ten. So each of these, each of these little hashmarks represent one hundredth. So one way you could view this is we're at two tenths, so we have two tenths, and then we're going to have one, two, three, four, five, six, seven hundredths. So we could view this point as two tenths and seven hundredths. So actually let me write it as a decimal first. So we have two tenths and we have seven hundredths. Now another way to think about this is we have 27 hundredth. You can count them. Remember each of these is one hundredth. So zero, one, two, three, four, five, six, seven, eight, nine, ten, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 27 hundredths. And most people when they see this number they won't say two tenths and seven hundredths. They'll just say 27 hundredths. Well how do you write 27 hundredths as a fraction? Well, it's 27/100. 27 over, over 100. Let's do, I don't know, I'm kind of in the mood. Let's do one more of these. The big square represents one whole. Express the shaded area as both a fraction and a decimal. So we've already seen, there's a hundred of these. The whole is split into a hundred equal, smaller sections. So each of these small squares is a hundredth and so how many hundredths do we have shaded in? So this is going to be ten hundredths, 20 hundredths, 21 hundredths. So as a fraction I'd write that as 21/100. Now, you could, there's a couple of ways to think about it. If we're familiar with it already we would say okay, look, two tenths is the same thing as 20 hundredths, so it's going to be two tenths and one hundredth, or 21 hundredth. Another way to think about it is this first row right over here, that's a tenth, then this next one is a tenth, so you have two tenths, and then you have a hundredth over here. So any way you want to think about it. This is 21 hundredths or two tenths and one hundredth.