Decomposing hundredths

- So this, this picture right over here, we've taken this square, we've divided it into 100 equal, smaller squares, and then we've colored in, let's see how many we've colored in. Each of these rows has 10 squares, so this is, 10, 20, 30, 40, 41, 42, 43, 44, 45, 46, 47. So over here, we have colored in 47 out of 100 equal, smaller squares. Or you could say that this, what's shaded in in blue and green right over here, this represents 47 hundredths. This is represents 47 hundredths of the entire, of the entire whole. Now what I'm curious about is, I wanna break up this fraction. I wanna write it as 40 over, actually lemme write it this way. I wanna write it as four over 10, plus, plus something over 100. And I'll just write star. Plus star over 100. And my question to you is, what is the star going to be equal to? The star is equal to what? And pause the video to try to figure it out. Alright, so let's, let's work this together. So one thing that we could say immediately, is we could say that 47 over 100 is equal to 40 hundredths, 40 hundredths. You see that over here, 10, 20, 30, 40 hundredths. This is 10, 20, 30, 40 hundredths, plus, one, two, three, four, five, six, seven hundredths. Plus seven hundredths. Now, 40 hundredths is the same thing as four tenths. 40 hundredths is the same thing as four tenths. There's a bunch of ways we could think about it. One is, you could think about dividing this larger, larger square into tenths, so this would be a tenth right over here, that would be a tenth, this would be another tenth, that's two tenths. This would be three tenths. And all I'm doing here, is I'm dividing the larger thing into tents, into tenths, I should say. If I'm taking the larger, if I'm taking the larger square, instead of dividing it into hundredths, I divide it into tenths. So this would be four tenths, (mumbles) doing five tenths, six tenths, six tenths, seven tenths, eight tenths, and nine tenths, and then 10 tenths. Notice, if you look at the orange lines, I've divided my square not into a hundred equal sections, but into ten equal sections. And so you see, these 40 hundredths that are in blue right over there, that's the same thing as one tenth, two tenths, three tenths, and four tenths. So that is the four tenths, right over there. Another way you could think about it, when you go from hundredths to tenths, each 10 hundredths, each 10 hundredths, is are equal to one tenth. So you're dividing both the denominator by 10, when you go from hundredths to tenths. And you'd also divide the numerator by 10, going from hundredths to tenths. So 40 divided by 10 is four, 100 divided by 10 is 10. So hopefully you're convinced that 40 hundredths is the same thing as four tenths. But what's left over? Well, we still have the seven hundredths over here. So 40 hundredths plus seven hundredths is the same thing as four tenths, plus seven hundredths. So the star right over here, this is going to, let me actually, let me erase this. The star right over here, I could write that as seven hundredths. So you see, 47 hundredths, which is all the stuff shaded, that's the same thing as the four tenths. Which is the same thing as 40 hundredths, shaded in blue. Plus these one, two, three, four, five, six, seven hundredths, right over here. 47 on 100, or 47 hundredths, 4 tenths, plus seven hundredths.