I’ll now show you how to convert a fraction into a decimal. And if we have time, maybe we’ll learn how to do a decimal in to a fraction.
So let's start with what I would say a fairly straight forward example. Let's start with the fraction ½ and I want to convert that into a decimal. The method I'm going to show you will always work. What you do is you take the denominator and you divide it into the numerator. Let's see how that works.
So we take the denominator, is 2. We’re going to divide that into the numerator, 1. You’ll probably say, well I how do I divide 2 into 1? Well, if you remember from the dividing decimals module, you can design a decimal right here and add some trailing zeros. Alright, we haven’t actually change the value of the number, were just getting some precision here. we put the decimal point here, 2 does go into 1, no. 2 goes into 10, so we go 2 goes into 10, 5 times. 5 times 2 is 10. Remainder 0. We’re done. So ½ is equal to .5.
Let's do a slightly harder one, let's figure out 1/3. Well once again, we take the denominator 3 and we divide it into the numerator. I’ll just add a bunch of trailing zeros here. Well 3 doesn’t go into 1, 3 goes into 10, 3 times. 3 times 3 is 9. Subtract. Get 1, bring down the 0. 3 goes into 10, 3 times. Actually this decimal point is right here. 3 times 3 is 9. Okay, do you see a pattern here? We keep getting the same thing. You can see it’s actually .3333, it goes on forever. And a way to actually represent this is, obviously you can't write an infinite numbers of 3, is you could just write .33 repeating which means that the .3 will go on forever. Or you can actually even say .3 repeating. Although I tend to see this more often. Maybe I'm just mistaken. But in general this line on top of the decimal means that this number pattern repeats indefinitely. So 1/3 is equal to .3333 and goes on forever and that’s equal to, another way of writing that is .33 repeating.
Let's do a couple of maybe a little bit harder, but they all follow the same pattern. Let me pick some weird numbers, let me say, let me do an improper fraction. Let me say 17/9. So here, it’s interesting, the numerator is bigger than the denominator. So actually were going to get a number larger than 1. But let's work it out. So we take 9 and we divide it into 17, let's add some trailing zeros. Put a decimal point here. So 9 goes into17, 1 time. 1 times 9 is 9. 17 minus 9 is 8. Bring down a zero, 9 goes into 80. Well, you know 9 times 9 is 81, so it has to go it only 8 times. 8 times 9 is 72. 80 minus 72 is 8. Bring down this zero. I think we see a pattern forming again. 9 goes into 80, 8 times. 8 times 9 is 72. If I keep doing this for ever, and we keep getting 8. So you see, 17 divided by 9 is equal to 1.88. Well the .88 is actually repeats forever. Or if we actually we want to round this, we can say that that is also equal to 1, depending on where we want to round it. We can say roughly 1.89 or we can round it in different place. I round it in the hundredths place. But this is actually the exact answer, 17/9 is equal to 1.88. Actually.
I’ll do it in separate module, but how would we write this in mix number? Well, actually I'm going to do it in a separate, I don’t want to confuse you for now. Let’s do a couple more problems.
Let me do a really weird one. Let me do 17/93. What does that equal as a decimal? Well we do the same thing. 93 goes into, I make a really long line up here because I don’t know how many decimal places will do it. And remember, it’s always the denominator being divided into the numerator. Because that confuse me a lot of times. Because you're often dividing the larger number into a smaller number. So 93 goes into 17, 0 times. Right? There is the decimal. 93 goes into 170, it goes in it 1 time. 1 times 93 is 93. 170 minus 93 is 77. Bring down the zero. 93 goes into 770, let's see, it will go into it 8 times? 8 times 3 is 24. 8 times 9 is 72 plus 2 is 74. And then we subtract, 26. And then we bring down the zero. 93 goes into 260, 2 times. 2 times 3 is 6. 18. This is 74. Zero. So we could keep going, this is actually, we could keep figuring out the decimal points. You could do this indefinitely. But if you want to get at least an approximation, we say 17 goes into 93 or 17/93 is equal to 0.182, and then the decimals will keep going. And you can keep doing it if you want. If you actually saw this in the exam, they probably tell you to stop at some point. You know, round it to the nearest hundredths or thousandths place.
And just so you know, let's try to convert it the other way, from decimals to fractions. And actually, this is I think you’ll find it much easier thing to do. If I were to ask you what .035 is as a fraction? Well, all you do is you say, well .035, that is the same thing as. We could write it this way, that’s the same thing as 35/1000. You're probably saying, Sal, how did you know its 35/1000? Well because this is the tenths place, this is hundredths, this is a thousandths place, right? So we went to 3 decimals of significance. So this is 35 thousandths. If the decimal was, if it was .030. There’s a couple of ways we can say this. Well we can say, oh, we got to 3, we went to the thousandths place. So this is the same thing as 30/1000. Or we could also said, well .030 is the same thing as .03, because this zero doesn’t have any value. So if we have .03, then we’re only going to the hundredths place. So this is the same thing as 3/100.
So let me ask you, are these two the same? Well yeah, sure they are. If we divide both the numerator and the denominator of both of these expressions by 10, we get 3/100. Well let's go back to this case, are we done with this? Is 35/1000, I mean its right. That is a fraction, 35/1000. If we want to simplify it more, looks like we could divide the numerator and the denominator by 5. And then just to get it into its simplest form, that equals 7/200. And if we want to convert 7/200 into a decimal using the technique we just did. So we would do 200 goes into 7 and figure it out. We should get .035. I’ll leave that up to you as an exercise.
Hopefully now you get at least an initial understanding of how to convert a fraction to a decimal and maybe vice versa. And if you don’t, just do some of the practices and I will also try to record another module on this or another presentation.
Have fun with the exercises.
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