Visually converting tenths and hundredths

0:00- [Voiceover] What I hope to do in this fraction is be able to rewrite the fraction 8/10 as being something over 100. So I could put a question mark here. I could put a star over here. Star over 100. And what I care about is figure out what is this star equal to.

0:17Eight over 10 is equal to what over 100? And I encourage you to pause the video to think about it. Now to help us work through this I have set up a little diagram, or actually two diagrams to think about what 8/10 looks like. And then I have the same whole, instead of being split into /10, I have it split up in /200.

0:40I have it spit up to 100 equal sections. And we just have to figure out how many of these 100 equal sections are equivalent to the eight out of the 10 equal sections right over here. So lets think about that a little bit. So once again, we have 10 equal sections here.

0:57And we have colored in one, let me mark'em all. If we've colored in one, two, three, four, five, six, seven, eight of them. This diagram, this picture, represents 8/10. 10 equal sections I have colored in eight of them. Now how do I do that if I'm talking about /100.

1:17Well it's the same whole right over here. Now if I want to fill up the same amount of that whole, so let me get a little paint brush here. So it would the the equivalent of 1/10 would be filling in 10/100. So that's 10/100 right over there. Then 2/10 or that second /10, every time I fill in a /10, that's the same thing as filling in 10/100.

1:43Let me write that down, cause that's interesting. So we see here that 1/10 is equal to 10 over 100. Every time I fill in a /10, that's 1/10 right over there. If you look at this diagram, that's the equivalent to 10/100. It's equivalent to 10 of those 100 equal sections.

2:05So if I wanna fill out 8/10, that's gonna be eight time 10/100 or 80/100. And lets just see that right over here. So we already did 10/100, 20/100. This is gonna be 30/100. 40/100. 50/100. 60/100. 70/100. And 80/100. Notice I've filled in the same amount, and I can fill it in just to make it a little bit clearer.

2:38But I filled in the same amount of both of these equal wholes. But over here, how many of these squares have I filled in? I have filled in 80, now let me get my pen going. I have over here, I have filled in 80 out of my 100 squares. While over here, I filled in eight out of my 10 equal rectangles.

3:02But they're the same amount of area. They're the same fraction of the whole. So eight over 10 is going to be the same thing as 80 over 100. You see it's the exact same thing. We've just divided the one on the right here into 10 times as many sections. And you can even see it mathematically.

3:20Then look, if we divided into 10 times as many sections. So, if we multiply a denominator by 10 to go from 10 to 100. Well that means that each of this eight sections in this one are going to represent 10 times as many in this one. So we would say, well, eight is going to represent 10 times as many of the /100.

3:40So eight times 10 is 80. 10 times 10 is 100. 8/10 is the same thing as 80/100. And in general, if you're trying to rewrite a fraction and not change its value, so you want an equivalent fraction, as long as you multiply the denominator, as long as you multiply the numerator and the denominator by the same thing, you will not be changing the value of the fraction.

4:05It's also true if you divide the numerator and the denominator by the same thing. You also will not be changing the value of the fraction. In this case we have multiply both the numerator and the denominator by 10. And you see why we did it.