In this section, we're going to start our work with percent. Now, percent means "per hundred." So, if I write 75% that means 75 per 100,
or 75/100; so, as a decimal, that's 0.75; or as a fraction, I could reduce it to 3/4.
So, 75%, 0.75, and 3/4 are all equivalent numbers because percent means per hundred.
So, what we want to do in this first section is just get used, get;
what we want to do is get used to converting back and forth between percent and decimals, and percent and fractions.
Let's look at our first example. We want to change to a decimal, and here, I have 23%. So, I'm going to write this as 23 per hundred,
meaning 23/100. Now, since I want to write this as a decimal, I'll convert this to 0.23. The next problem, I have 9%.
So, I'm going to write that as 9 per 100, or 9/100. Then, as a decimal, that's 0.09. So, 9% means 9 per 100, or 9/100 if I write it this way;
and then as a decimal, it's this. So, you can see, if I wanted to convert from this on to a fraction, I'd just leave it this way.
So, right now, we're converting to decimals, but I used that definition of percent as meaning "per hundred." Here's some more.
Here, I have 6.34%. I want to change that to a decimal. I'm going to use the same idea: 6.34 per hundred.
Now, when I divide 6.34/100, I get 0.0634. So, 0.0634 is the same as 6.34%. Now, my next problem, I have 0.9%.
Let's see what it looks like as a decimal. I use my same reasoning here. It's 0.9 per hundred, so over 100.
Now, when I divide 0.9/100, I get 0.009. So, 0.009 is the decimal equivalent of 0.9%.
The next problems we want to do, we're going to start with a decimal and change to a percent. Let's take a look at those.
For problem number 5, we want to change 0.45 to a percent. So, I know that 0.45 is 45 hundredths.
So, that means that this must be 45 per 100, or 45%. So, 0.45, that decimal as a percent is 45%.
Now, you can check to see if that makes sense by going back to 45/100, when I take my percent and write it as per hundred. And sure enough,
we get 0.45. So, here I have 0.03, so that's going to be 3%. So, one way to look at this, and starting with decimals,
when I want to change a decimal to a percent, I can simply move the decimal point two places to the right, and then attach a percent symbol.
So, 0.45, I'd go one, two places to the right, and I'd end up with 45; then, I attach the percent symbol.
Same with 0.3: I move that two places over, and I get 3, and then attach the percent symbol.
So, let's use that on our next two problems. I have 0.6; I want to change to a percent. So, I move one, two places over; I get 60,
and attach the percent symbol. So, 0.6 as a decimal is the same as 60%.
Now, 1.23: I'm going to move the decimal point two places to the right; I get 123, and then I attach my percent symbol.
So, 1.23 is the same as 123%. (So, let's go to the wide camera here for a second.) Okay, so 1.23 is the same as 123 percent.
So, when I have a number that's bigger than 1, I get a percent that's bigger than 100%. So, 0.6 = 60%; 1.23 = 123%.
The next thing we want to do is change some percents into fractions. Let's take a look at those. For problem number 9, we have 60%;
and we want to change that to a fraction. So, I'm going to write this using my definition as 60/100.
Then, I'll divide the numerator and denominator by 10; I'll get 6/10. Reducing to lowest terms: divide numerator and denominator by 2,
and I'll have 3/5. So, 60% as a fraction turns out to be 3/5. Let's try 4%, that's 4 per 100, or 4/100.
I'll divide the numerator and denominator by 4, and I'll get 1/25. So, that is the fraction 1/25. Now, how about 6 1/4 percent?
Let's just keep doing what we were doing. 6 1/4 ÷ 100. Okay, let's try to change this to an improper fraction:
4(6) = 24, 24 + 1 = 25 over 4 for the numerator; and then, instead of dividing by 100, let's multiply by 1/100.
So, instead of dividing by 100, I multiply by its reciprocal 1/100. The 25's divide out, and I end up with 1/16.
So, this one, 1/16, that's the fraction equivalent of 6 1/4%; that's 1/16.
4% is the same as 1/25; and 60% is the same as 3/5. So, you can see, in each of these cases, when I change my percent to a fraction,
what I do is just use my definition to write it with a denominator of 100.
And then, I do whatever I can mathematically to change it into just a simple fraction. Let's try one more example: 0.75%.
I'm going to write this as 0.75 per hundred, or over 100. Now, it's hard for me to work with decimals and fractions in the same thing.
So, I'm going to multiply the numerator and denominator of this by 100, so, I can move this decimal point over;
I end up with 75 ÷ 1, and let's see, 1, 2, 3, 4 0's, so, 75/10,000.
If I divide 25 into the numerator, it will go 3 times. If I divide 25 into the denominator, it should go 400 times.
So, I end up with 3/400 for the fraction that's equivalent to 0.75%. Now, I want to work a couple of more problems on this,
but I'm out of board space. So, I'm going to walk over here to the other board and show you those. Here we go.
We want to change to percent now from a fraction. So, problem 13, I have 3/4, and I want to write that as a percent.
Now, if I can change this to a decimal, and you may recall that 3/4 is the same as 0.75, if I've got it as a decimal,
then I know that that's going to be equal to 75 percent. So, how to get it to the 0.75? Well, there's a couple of ways.
One thing I can do is multiply the numerator by 25 and the denominator by 25. And then, that would be 75/100, which is either 0.75 or 75%.
Another way to do it would be to take 4 and divide it into 3 to get that decimal. So, I'll put some 0's in. 4 goes into 30, let's see, 7 times;
7(4) = 28; subtract, I get 20; 4 goes into 20, 5 times; so, 0.75. A couple of different ways to do a problem like this:
I can multiply numerator and denominator by 25, change to this fraction over 100, that's 75%;
or I could divide the denominator into the numerator and actually get 0.75, and then just change that to 75%.
We improvised a little bit. Let's try another one: 4/5. Now, how about if we try to write this as something over 100?
Well, what would I multiply 5 by to get 100? The answer would be 20. So, if I multiply the denominator by 20,
I do the same thing to the numerator: 4(20) = 80, and so, that I know to be 80%.
Another way to do the same problem would be to divide 5 into 4; you'd get 0.80, which you change to a percent. You still get 80 percent.
Here's another problem: 7 ÷ 8. Let's try this one with division. So, I'm going to divide 8 into 7.000; I'll give myself enough 0's to work.
8 goes into 7, let's see, how about 8(8) = 64; I'll subtract and get 6; bring down the 0. 8(7) = 56; subtract and get 4.
8 goes into 40, 5 times. So, 0.875 as a decimal, and that's going to give me 87.5 as a percent; so, 87.5%.
So, here's a problem that's easiest to do if we actually do that division. I divide 8 into 7; its division yields 0.875.
I change that decimal to a percent; I get 87.5 percent. Here's another problem. 3 1/4. Well, let's see, a couple of ways to do this;
let's try to change this to an improper fraction, that's one way: 4(3) = 12, 12 + 1 = 13. So, that's 13/4.
So, let's divide 4 into 13 and see what happens. So, 4 into 13, and I'm going to have, put a couple of 0's in. 4 goes into 13, let's see, 3 times?
And I get 12; subtract, and I get 10; 4 divides into there twice; 2(4) = 8; subtract and get that. 4 divides into there 5 times; I get 3.25.
So, 4 1/4, 13/4, that's 3.25. I could have just changed that 1/4 into 0.25, also. Either way, I get 3.25, changing that decimal to a percent.
I get 325% because I move the decimal point two places to the right and attach a percent symbol.
And that's right because this number is larger than 1. So, as a percent, it's going to be larger than 100 percent.
So, there's a look at the conversions that are involved in going between percent and fractions, and percent and decimals.