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Write 18% as a decimal and as a fraction in simplest form.

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So let's do it as a decimal first. So 18% is the same

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thing as 18 per 100, or 18 per cent.

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I'm actually separating out the percent, it's only going

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to be one word, but I'm writing it as,

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literally, per cent.

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Cent means the same thing as 100.

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So this literally means 18 per 100.

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Actually, I said I would do the decimal first, but we can

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start putting it into a fraction first. 18 per 100 as

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a fraction literally means 18/100.

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We're literally doing the fraction first. This literally

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means 18 per 100, or 18 hundredths.

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From here we can go straight to a decimal or we could do

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this fraction in simplest form.

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Let's do the decimal first, just because that's actually

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what I said I would do first. Let's do that first. This is

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the same thing as 18 hundredths.

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And we know how to write that in decimal form.

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It's 0.18.

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You could view this as 1 tenth and 8 hundredths, which is the

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same thing, or 10 hundredths and 8 hundredths, which is 18

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hundredths.

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So this is written in decimal form.

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And if we write it as a simplified fraction, we need

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to see if there is a common factor for 18 and 100.

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And they're both even numbers, so we know they're both

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divisible by 2, so let's divide both the numerator and

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the denominator by 2.

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So we have 18 divided by 2 over 100 divided by 2.

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And we're going to get 18 divided by 2 is 9.

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100 divided by 2 is 50.

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And I don't think these guys share any common factors.

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50 is not divisible by 3.

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9 is only divisible by 3 and 1 and 9.

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So this is the fraction in simplest form.

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So we have 18% is the same thing as 0.18, which is the

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same thing, in simplest form, as 9/50.

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Now, I went through a lot of pain here to show you that

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this really just comes from the word, from

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percent, from per 100.

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But if you ever were to see this in a problem, the fast

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way to do this is to immediately say, OK, if I have

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18%, you should immediately say, anything in front of the

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percent-- that's that anything, whatever this

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anything is-- it should be equal to that anything.

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In this case it's 18/100.

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And another way to think about it, you could

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view this as 18.0%.

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I just added a trailing zero there, just so that you see

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the decimal, really.

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But if you want to express this as a decimal without the

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percent, you just move the decimal to

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the left two spaces.

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So if we move the decimal to the left two spaces, one, two,

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this becomes 0.18.

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Or you could immediately say that 18% as

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a fraction is 18/100.

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When you put it in simplified form, it's 9/50.

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But you should also see that 18/100, and we have seen this,

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is the exact same thing as 18 hundredths, or 0.18.

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Hopefully, this made some connections for you and didn't

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confuse you.

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