Intro to percentages
Representing a number as a decimal, percent, and fraction 2 Representing a number as a decimal, percent, and fraction 2
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- We're asked to write 7/8 as a decimal and as a percent.
- We'll start off with a decimal, and we'll see it's
- pretty easy to go from a decimal to a percent.
- Now, whenever you see a problem like this, it's
- sometimes confusing.
- It's like, how do I even get it into a decimal, or as a
- fraction over 100, or as a percentage?
- And you always have to remember 7 over 8, or 7/8, is
- the exact same thing.
- This means literally 7 divided by 8.
- Not 8 divided by 7.
- 7 divided by 8.
- The numerator divided by the denominator.
- And you say, well, how do I turn that into a decimal?
- Well, we just literally do a long division problem, but we
- keep going behind the decimal point, so that we don't end up
- with a remainder, or until we end up with things repeating.
- You'll see what we mean.
- In this case, we won't end up with anything repeating.
- So let's try this out.
- So it's 7 divided by 8.
- So how many times does 8 go into 7?
- Well, 8 does not go into 7.
- It goes zero times.
- And actually, just so that we make sure that everything's
- clean, let's put our decimal.
- You can view this as 8 going into 7.000.
- You can keep adding as many zeroes as you need until
- you're done dividing.
- So we have our decimal point right here, right behind the 7
- where it was up here.
- So we say 8 goes into 7 zero times.
- 0 times 8 is 0.
- You subtract.
- 7 minus 0 is 7.
- Now we can bring down a 0.
- We bring down a 0.
- It becomes 70.
- And then you say 8 goes into 70 how many times?
- Well, 8 times 8 is 64, so that works.
- 8 times 9 is 72.
- That's too big.
- So it goes into it eight times.
- 8 times 8 is 64.
- When you subtract, 70 minus 64 is 6.
- You still have a remainder, so let's keep going.
- Let's bring down another 0.
- So you bring down another 0 right over there, and so you
- say, how many times does 8 go into 60?
- 8 times 8 is 64, so that's too big.
- 8 times 7 is 56, so that'll work.
- So it goes into 60 seven times.
- 7 times 8 is 56.
- You subtract.
- 60 minus 56 is 4.
- So we still have a remainder, so let's keep bringing down
- some zeroes.
- So let's bring this 0 down here.
- And 8 goes into 40 how many times?
- Well, 8 times 5 is 40, so it goes in nice and evenly.
- So it goes into it five times.
- 5 times 8 is 40.
- Subtract.
- No remainder.
- So as a decimal, we just figured out that 7/8, which is
- equal to 7 divided by 8, is exactly 0.875.
- So 7/8 as a decimal is equal to 0.875.
- Now we've done the decimal part.
- Now the next thing is to do a percent.
- And if you have it as a decimal, doing it as a percent
- is very easy.
- You literally shift the decimal place two to the
- right, and you put a percent sign there.
- And I think it makes sense why it works.
- Now you're going to say, how many per hundred?
- You can view this as 875 thousandths.
- Let me write this down.
- You can view this as a fraction.
- You could say, well, this is the same thing as 875/1,000.
- That's how we've read it in the past. This is the
- thousandths spot right here.
- Or you could read this as 87.5/100.
- If you just go two decimal places, it's 87.5/100.
- Or if you just took this, and you divide the numerator and
- the denominator by 10, you would get this.
- And this is literally saying 87.5 per 100, So this second
- statement right here, this is literally saying 87.5 per
- hundred, or per cent.
- So this is equal to 87.5%.
- So that gives you the reasoning for why it works,
- but the really easy way, if you have a decimal, to make it
- into a percent, you literally multiply the number by 100 and
- put the percent there, which is essentially telling you
- that you're going to divide by 100, so you're multiplying and
- dividing by 100.
- So if you multiply this by 100, which is equivalent to
- shifting the decimal place two places to the right, that
- literally would become 87.5, then you
- want to put the percent.
- This says this is going to be over 100.
- So you multiply by 100, and then divide by 100.
- You're not really changing the number.
- Hopefully, that makes sense.
- Another way to remember, because sometimes you might
- get confused-- Do I put the decimal to the right?
- Do I take it to the left-- is that the decimal
- representation will always be smaller than the percent
- representation.
- And not only will it be smaller, but it will be
- smaller by exactly a factor of 100.
- This is 100 times smaller of a number right here
- than just the 87.5.
- Obviously, when you put this percent here, these become the
- exact same number.
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