
Title:
Percents  Visualizing Algebra

Description:

We're done working with exponents for now, but we'll come back to them later.

Let's look at some other ways that we can use decimals. We're going to look at

decimals and percents. Decimals and percents are often used in currency and in

commercial business. We can buy shoes, sweaters, or electronics on sale. And we

often want to know how much does something actually cost. By the end of this

segment, you'll be able to find out how much an item cost, like a new pair of

shoes. So, here's the problem that we're going to have you answer and come back

to later. A pair of shoes costs $80 and is on sale for 44% off, what will you

pay for the shoes? The first thing we need to recognize is this problem has a

percent in it. Percent literally means per 100 or out of a 100. I can write

44 percent another way.

I know it's 44 out of 100 or 44 divided by 100. 44 divided by 100 is the same

thing as 0.44. Here's a grid of a 100 squares, or I have 1 block. Of these 100

pieces, I'm going to have 44 of them. So, I'd have 10, 20, 30, 40, 44 blocks out

of a 100 or 0.44 and that's this written as a decimal, 0.44. Okay, here are some

other percents. I can have 23%, 6%, or 200%.

I'm going to convert these percents to decimals. Sometimes, we need to convert

percents to decimals in order to use them in problems or to multiply. Okay, so

let's use these 100 blocks to help us out. Here, I have 23 squares shaded out of

100. So, 23 divided by 100. As a decimal, that's 0.23. For 6%, I'm going to have

6 blocks out of a 100. So, I have 6 blocks out of a 100 or 6 hundredths, 0.06

Notice that 6 has to be in the hundredths spot. For 200%, I know that I have to

do something different. I can color in 100 of the squares in this 1 block. So, I

have a 100 blocks shaded, but I need 200%. This is only a hundred out of a

hundred, that's a 100%. 200 percent means 200 out of 100. I know one of these

squares represents a hundredth, so I have 200 hundred hundredths, or I just have

2 or 2 blocks. Okay. There's actually a pattern here that we want to notice.

Let's look closely at the decimal places. Here in 23%, the decimal is here and

then it ended up here. For 6%, the decimal started here and ended up here. For

200%, the decimal started here and ended up there.

Let's have a quiz behind what's going on with this pattern. What do you notice?