Equivalent representations of percent problems
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Write 18% as a decimal and as a fraction in simplest form. So let's do it as a decimal first. So 18% is the same thing as 18 per 100, or 18 per cent. I'm actually separating out the percent, it's only going to be one word, but I'm writing it as, literally, per cent. Cent means the same thing as 100. So this literally means 18 per 100. Actually, I said I would do the decimal first, but we can start putting it into a fraction first. 18 per 100 as a fraction literally means 18/100. We're literally doing the fraction first. This literally means 18 per 100, or 18 hundredths. From here we can go straight to a decimal or we could do this fraction in simplest form. Let's do the decimal first, just because that's actually what I said I would do first. Let's do that first. This is the same thing as 18 hundredths. And we know how to write that in decimal form. It's 0.18. You could view this as 1 tenth and 8 hundredths, which is the same thing, or 10 hundredths and 8 hundredths, which is 18 hundredths. So this is written in decimal form. And if we write it as a simplified fraction, we need to see if there is a common factor for 18 and 100. And they're both even numbers, so we know they're both divisible by 2, so let's divide both the numerator and the denominator by 2. So we have 18 divided by 2 over 100 divided by 2. And we're going to get 18 divided by 2 is 9. 100 divided by 2 is 50. And I don't think these guys share any common factors. 50 is not divisible by 3. 9 is only divisible by 3 and 1 and 9. So this is the fraction in simplest form. So we have 18% is the same thing as 0.18, which is the same thing, in simplest form, as 9/50. Now, I went through a lot of pain here to show you that this really just comes from the word, from percent, from per 100. But if you ever were to see this in a problem, the fast way to do this is to immediately say, OK, if I have 18%, you should immediately say, anything in front of the percent-- that's that anything, whatever this anything is-- it should be equal to that anything. In this case it's 18/100. And another way to think about it, you could view this as 18.0%. I just added a trailing zero there, just so that you see the decimal, really. But if you want to express this as a decimal without the percent, you just move the decimal to the left two spaces. So if we move the decimal to the left two spaces, one, two, this becomes 0.18. Or you could immediately say that 18% as a fraction is 18/100. When you put it in simplified form, it's 9/50. But you should also see that 18/100, and we have seen this, is the exact same thing as 18 hundredths, or 0.18. Hopefully, this made some connections for you and didn't confuse you.