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Contents

## Percents

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 cost \$80 and is on sale for 44% off, what will you pay for the shoes? The first thing that we need to recognize is that this problem has a percent in it. Percent literally means per 100, or out of 100. I can write 44% another way. I know it's 44 out of 100, or 44 / 100. 44/100 is the same thing as 0.44. Here's a grid of 100 squares, or I have one 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 decimal, 0.44. Okay here are some other percents. I could 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 lets use these 100 blocks to help us out. Here I have 23 squares shaded out of 100, so 23 / 100. As a decimal, thats 23.. For 6%, I'm going to have 6 blocks out of 100. I have 6 blocks, out of 100 or 06. or 06.. Notice that the 6 has to be in the hundredths spot. For 200%, I know that I have to do something different. I could color in 100 of the squares in this one block. So, I have a hundred blocks shaded, but I need 200%. This is only a hundred out of hundred. That's a hundred percent. these squares represents a hundredth, so I have 200 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 a t 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?

## how does the decimal move

Okay. When converting a percent to a decimal, do we add, subtract or divide by ahead, make your choices.

## how does the decimal move

I know, based on our models, we have to divide by 100, so division is correct and when I look at the decimal, here it moved it moved 2 places left.

## Decimal to Percent

Remember in math we want to be able to work forwards and we also want to work backwards. Sometimes it's helpful to convert back to a percent. To get back to a percentage I would undo the percent. I know that percent means divide by a hundred and I want to undo this. So to undo dividing my 100 I have to multiply by decimal place two places to the right. This should make sense because we can remember that multiplying by 100, is the same as multiplying by 10^2. I'm going to move my decimal two places to the right, because the exponent's postive. So I'll get 23%, .06 would turn back into

## decimal to percent quiz

Here are some decimals, and I want you to change them to percents. I've already written the percent symbol for you. You want to enter your numbers in these boxes. Remember, when you're doing your math, you always want to write percent.

## decimal to percent quiz

We want to go from a decimal to a percent, so I need to move the decimal two places to the right. I need to multiply by 100, and I get 33%. For 25 thousandths, I need to move the decimal two places to the right. That's multiplying by 100, and I get 2.5%. For 3 and 125 thousandths, I still need to move the decimal 2 places to the right. That's the same thing as multiplying by 100, so, I'll have 312 and moved the decimal 2 places by multiplying by 100, and I get .04%. Nice work on that quiz.

## converting decimals and percents

Remember we want to be able to go between decimals and percents. Alright, here's some percents and here's some decimals, for this quiz I want you to fill in the boxes with the appropriate decimal or percent. You'll need to convert either to a decimal, or to a percent. And again with the percents don't worry about entering percents, I've already done it for you. Just enter the numbers.

## converting decimals and percents

So for 60%, I want to do percent or divide it by 100. I know dividing by 100 moves the decimal place two places left so I get percents, I'm going to need to move the decimal two places left and divide it by again, I'm going to move the decimal two places left. And I get .5302, here when I move the decimal 2 places left I get 2 extra 0's and my decimal point ends up here. So I get this number. Again I move the decimal 2 places left and I wind up with 30. It's probably easier to remember how to go from a percent to a decimal, you just think about what the word percent means, it means per 100 or divided by 100. So to go from a decimal to a percent, we need to undo that dividing by 100. So we multiply by 100. So, 52100=5,200%. Multiplying .004100 gives me .4 percent and 1.35 /100 gives me a 135%. Notice that each time I convert a decimal to a percent, the decimal place moves 2 places to the right. Now that we can work with decimals and percents, let's go back to our shoe problem.

## Discounted Shoes Easier

And we're going to do a strategy that we've done before. Let's look at a simpler version of the problem. A pair of shoes costs \$60 and is on sale for 20% off, what will you pay for the shoes? The key thing is that we do not pay 100% of the price. If we did paya 100% of the price, our Math would look like this. We'd have \$60100%. I know percent means out of 100. So I have Well, I know 100/100 is just 1, so I have I could've just gotten that by moving my decimal two places to the left. We know dividing by 100 is the same thing as moving the decimal two places left, so I would owe \$60. Notice if you have 100% of something, the value doesn't change. My price originally was \$60, and if I pay

## what percent do you pay

For the quiz, what percent of the price do you pay for the pair of shoes? Put your answer in this box, and don't worry about typing the percent. I've already written the symbol for you.

## what percent do you pay

I know if I paid the full price of the shoes I would have to pay 100%. But I get I'm going to show you how to finish this problem out. So I have 80% of the original cost, so at 80% times the original cost which is \$60. I'm going to change my percent to a decimal. I know I need to divide by 100 because it's percent, so I move the decimal two places to the left. I get 0.8 \$60. I'm going to do \$0.8 \$60, I get \$48. So I only have to pay \$48 to get the shoes. That's a pretty good deal. Okay, let's try another problem.

## Increasing Shoe Stock

Your favorite shoe company only has 200 pairs of shoes in stock, shoes are selling fast because of the sale. If the company increases its shoe inventory by 25%, how many pairs of shoes will the company have? So the company is going to be running out of shoes. If the company doesn't get any new pairs of shoes. They'll have 100% of their inventory. Their current inventory is 200, so they'd have 100% of 200. I know that as a decimal 100% is just 1. I divide by 100 and move the decimal place left. So I have 1 200. The company doesn't want this. If they just have 100% of the shoes their inventory won't change and they'll run out of shoes. So, in the last problem we had to decrease our percentage because we had a percent off, but this time the company wants to increase their percentage. Let's see if you can figure out what percentage of the pairs of shoes you actually want to find.

## more shoes

So, what percentage should the company multiply by 200, the current inventory of shoes, to get more pairs of shoes? Put your answer in this box and leave out the percent sign, I've already written it here.

## more shoes

We know if we use 100%, the company will keep it's 200 pairs of shoes. We want to increase this number, so, we need to multiply by a number bigger than 100%. They want to increase their inventory by let's actually see this problem worked out. I want to take 125% of the inventory. So I have 125%. Of is times the inventory, which is 200 pairs of shoes for my company. I know % means divide by 100, so I move the decimal place 2 places to the left. I have 1.25 times 200. When I multiply, I get 250 pairs of shoes. Okay, this is great, and we can actually make sense of this another way. We can think of going to add another 50. So I have 50 and which is 200 and 50 more, which is 250. If you could reason through percentages like that in your head, that's great. If not you can always rely on the math.