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I'll now show you how to convert a fraction

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into a decimal.

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And if we have time, maybe we'll learn how to do a

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decimal into a fraction.

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So let's start with, what I would say, is a fairly

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straightforward example.

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Let's start with the fraction 1/2.

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And I want to convert that into a decimal.

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So the method I'm going to show you will always work.

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What you do is you take the denominator and you divide

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it into the numerator.

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Let's see how that works.

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So we take the denominator-- is 2-- and we're going to divide

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that into the numerator, 1.

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And you're probably saying, well, how do I divide 2 into 1?

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Well, if you remember from the dividing decimals module, we

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can just add a decimal point here and add some trailing 0's.

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We haven't actually changed the value of the number, but we're

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just getting some precision here.

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We put the decimal point here.

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Does 2 go into 1?

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No.

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2 goes into 10, so we go 2 goes into 10 five times.

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5 times 2 is 10.

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Remainder of 0.

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We're done.

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So 1/2 is equal to 0.5.

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Let's do a slightly harder one.

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Let's figure out 1/3.

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Well, once again, we take the denominator, 3, and we divide

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it into the numerator.

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And I'm just going to add a bunch of trailing 0's here.

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3 goes into-- well, 3 doesn't go into 1.

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3 goes into 10 three times.

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3 times 3 is 9.

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Let's subtract, get a 1, bring down the 0.

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3 goes into 10 three times.

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Actually, this decimal point is right here.

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3 times 3 is 9.

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Do you see a pattern here?

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We keep getting the same thing.

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As you see it's actually 0.3333.

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It goes on forever.

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And a way to actually represent this, obviously you can't write

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an infinite number of 3's.

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Is you could just write 0.-- well, you could write 0.33

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repeating, which means that the 0.33 will go on forever.

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Or you can actually even say 0.3 repeating.

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Although I tend to see this more often.

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Maybe I'm just mistaken.

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But in general, this line on top of the decimal means

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that this number pattern repeats indefinitely.

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So 1/3 is equal to 0.33333 and it goes on forever.

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Another way of writing that is 0.33 repeating.

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Let's do a couple of, maybe a little bit harder, but they

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all follow the same pattern.

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Let me pick some weird numbers.

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Let me actually do an improper fraction.

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Let me say 17/9.

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So here, it's interesting.

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The numerator is bigger than the denominator.

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So actually we're going to get a number larger than 1.

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But let's work it out.

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So we take 9 and we divide it into 17.

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And let's add some trailing 0's for the decimal point here.

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So 9 goes into 17 one time.

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1 times 9 is 9.

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17 minus 9 is 8.

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Bring down a 0.

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9 goes into 80-- well, we know that 9 times 9 is 81, so it has

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to go into it only eight times because it can't go

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into it nine times.

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8 times 9 is 72.

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80 minus 72 is 8.

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Bring down another 0.

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I think we see a pattern forming again.

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9 goes into 80 eight times.

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8 times 9 is 72.

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And clearly, I could keep doing this forever and

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we'd keep getting 8's.

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So we see 17 divided by 9 is equal to 1.88 where the 0.88

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actually repeats forever.

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Or, if we actually wanted to round this we could say that

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that is also equal to 1.-- depending where we wanted

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to round it, what place.

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We could say roughly 1.89.

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Or we could round in a different place.

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I rounded in the 100's place.

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But this is actually the exact answer.

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17/9 is equal to 1.88.

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I actually might do a separate module, but how would we write

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this as a mixed number?

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Well actually, I'm going to do that in a separate.

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I don't want to confuse you for now.

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Let's do a couple more problems.

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Let me do a real weird one.

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Let me do 17/93.

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What does that equal as a decimal?

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Well, we do the same thing.

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93 goes into-- I make a really long line up here because

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I don't know how many decimal places we'll do.

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And remember, it's always the denominator being divided

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into the numerator.

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This used to confuse me a lot of times because you're often

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dividing a larger number into a smaller number.

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So 93 goes into 17 zero times.

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There's a decimal.

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93 goes into 170?

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Goes into it one time.

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1 times 93 is 93.

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170 minus 93 is 77.

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Bring down the 0.

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93 goes into 770?

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Let's see.

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It will go into it, I think, roughly eight times.

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8 times 3 is 24.

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8 times 9 is 72.

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Plus 2 is 74.

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And then we subtract.

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10 and 6.

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It's equal to 26.

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Then we bring down another 0.

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93 goes into 26-- about two times.

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2 times 3 is 6.

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18.

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This is 74.

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0.

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So we could keep going.

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We could keep figuring out the decimal points.

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You could do this indefinitely.

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But if you wanted to at least get an approximation, you would

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say 17 goes into 93 0.-- or 17/93 is equal to 0.182 and

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then the decimals will keep going.

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And you can keep doing it if you want.

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If you actually saw this on exam they'd probably tell

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you to stop at some point.

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You know, round it to the nearest hundredths or

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thousandths place.

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And just so you know, let's try to convert it the other way,

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from decimals to fractions.

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Actually, this is, I think, you'll find a

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much easier thing to do.

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If I were to ask you what 0.035 is as a fraction?

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Well, all you do is you say, well, 0.035, we could write it

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this way-- we could write that's the same thing as 03--

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well, I shouldn't write 035.

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That's the same thing as 35/1,000.

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And you're probably saying, Sal, how did

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you know it's 35/1000?

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Well because we went to 3-- this is the 10's place.

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Tenths not 10's.

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This is hundreths.

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This is the thousandths place.

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So we went to 3 decimals of significance.

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So this is 35 thousandths.

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If the decimal was let's say, if it was 0.030.

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There's a couple of ways we could say this.

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Well, we could say, oh well we got to 3-- we went to

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the thousandths Place.

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So this is the same thing as 30/1,000.

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or.

170
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We could have also said, well, 0.030 is the same thing as

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0.03 because this 0 really doesn't add any value.

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If we have 0.03 then we're only going to the hundredths place.

173
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So this is the same thing as 3/100.

174
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So let me ask you, are these two the same?

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176
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Well, yeah.

177
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Sure they are.

178
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If we divide both the numerator and the denominator of both of

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these expressions by 10 we get 3/100.

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Let's go back to this case.

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Are we done with this?

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Is 35/1,000-- I mean, it's right.

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That is a fraction.

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35/1,000.

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But if we wanted to simplify it even more looks like we could

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divide both the numerator and the denominator by 5.

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And then, just to get it into simplest form,

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that equals 7/200.

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And if we wanted to convert 7/200 into a decimal using the

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technique we just did, so we would do 200 goes into

191
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7 and figure it out.

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We should get 0.035.

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I'll leave that up to you as an exercise.

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Hopefully now you get at least an initial understanding of how

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to convert a fraction into a decimal and maybe vice versa.

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And if you don't, just do some of the practices.

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And I will also try to record another module on this

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or another presentation.

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Have fun with the exercises.

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