in-13-22-write-each-decimal-as-a-common-fraction-0-overline108

Question

In $13-22,$ write each decimal as a common fraction.
$$
0 . \overline{108}
$$

Bahar Tehranipoor · Accepted Answer

and this question we want to write this estimate was a common fraction. So we&#x27;ll use a trick to race with this equal to X now. To get rid of the repeating part we can do is we can multiply by 1000. So if we have 1000 X, that would be not 1.10 air. Whatever peeing it&#x27;ll give us that 108 0.108 Repeating because if this is X and we&#x27;ll buy 10 we&#x27;re not going to get something that cancels out for most of my 100 bogus make ends up. But if you want to buy 1000 you can get that one way out and still have 10.1 await Repeating. Now, if we subtract these two things, we&#x27;re going to get 1000 x minus. Extras will give us 999 X now 108.1 of repeating minus. Just point. What about repeating? We&#x27;re going to get 108 and now very easily. We could just say X equals 18 over 999 We can simplify this. Don&#x27;t want to go through the work of the show you what it is. If you simplify it, you get for over 37

Martha Richards · Answer

take the decimal 0.36 where this three sex repeats and turn it into a fraction. And we do that by getting, um by multiplying by 100 so that we encompass the total of the repeating decimals. So also axe equal to this. And then I say, ah 100 x is equal to So if I multiply by 100 that means I move the decimal 1000.2 to the right. And so now I&#x27;m encompassing the entirety of the repeating decimals. So I get 36 point 36 in this 36 Repeat. Now I want to subtract out that 360.3 sex. So all I have to do then is subtract X. And when I subtract X, I&#x27;m subtracting 0.36 So now you see everything to the right of the decimal. When I subtract, will disappear, so that will become zero. And then I end up with 36. And when I subtract this, I end up with 99 X now to solve for X, I get 99 divided on both sides. And so I get X is equal to 36 over 99. What we see here that both of these air divisible by nine. So I get a four in the numerator and 11 in the denominator

Bahar Tehranipoor · Answer

and this question we want to write this estimate was a common fraction, and there&#x27;s a really cool trick used to do this. So we consider that original value is X, and we want to do is we want to make it so that we can have two values that if we subtract, we can get rid of this repeating part, and it&#x27;s much easier for it to show you rather than explain. So if we have this original value as X, if we have 10 X, we just want to attend. We get 1.36 still repeating now to take that three x out. What we can do is we could do something like 1000 X that is going to equal 136.36 repeating now, as you can see, if we subtract thes two things, we get rid of this repeating parts. So that&#x27;s the trick. You just get rid of the repeating part, so if you subtract, you get 1 35 equals 990 x. So we have that X equals 1 35 over 90 and that&#x27;s pretty much it. That&#x27;s how you find your desperate was a common fraction. But of course you can simplify this more, and if we take all the factors out, we&#x27;re left with three over 22.

Bahar Tehranipoor · Answer

in this exercise we want to write. This decimal is a common fraction, so let&#x27;s use a trick. Voices ableto x What 10 we get 10 X equals 2.2 repeating. And now we can subtract these two from each other to get our answer. So 10 X minus X would get with Nynex and then 2.2 repeating minus point to repeating would just give us two. We divide both sides by nine. We get X equals to over nine. So our original, uh, does well here. We can write it as to overnight.

Martha Richards · Answer

Okay, So what we want to do is switch this repeating decimals into a fraction. And the way that you do this is we&#x27;re going to say we&#x27;re gonna let X equal to this 0.6 that repeats. So when you only have it repeating in the 10th position if you multiply that by 10. 10 x So if I multiply this by ton, remember and move this one decimal place. So this and remember, this continues to repeat, Repeat, repeat. So this 10 Times X is equal to 6.66 And this keeps going on. And then if I subtract acts from both sides so here I would say remember that X was equal to this. So we&#x27;ll put those equal there. And then when I subtract all of this stuff here, cancels out because we&#x27;re subtracting and ex from this side and subtracting X from the side. And so when I subtract, I end up with six by itself. Here I&#x27;d get nine. X is equal to six to solve for X on Divide both sides by nine and you can see that this will reduce so I can divide top and bottom by three and I get 2/3. And if you use your calculator, you&#x27;ll see that 2/3 indeed gives us this.

Bahar Tehranipoor · Answer

in this question we want to write. This decimal is a common fraction, and this one might look pretty familiar to some of you just because if you plugged something into a calculator before this may have come up, so when you see the answer, it&#x27;ll look very familiar. So the first thing I want to do is use this trick or just set this equal to X. Now if we want Webber 10 so we have 10 X, we get 8.3 repeating. No, let&#x27;s multiply it by hundreds. We have 100 X equals 83 0.3. Repeating now for subtract these two. We get rid of that repeating part, which is very convenient in ah, cool trick that we can use to find an answer. So if we subtract, we&#x27;re gonna get 90 x source attracting in the opposite direction. So 90 x now 83.3. Repeating minus 8.3 Repeating the three repeating part is gonna get rid of it. Get rid of selfish who disappears. We have 83 minus eight, which is going to give us 75. It was an equal 75. Now we have X equals 75 over 90. So what can we divide out here? We can very easily see. We could find out of fives. We have 15 over 90 over. I will be 18. Now. If we divide out a three, we&#x27;re gonna have five over six. So our answer is five or six. And as I was saying, this one looks really familiar. Ifyou&#x27;ve divided 5 to 6 into a calculator, you have most likely seen 60.8 through your beating.

Problem

In $13-22,$ write each decimal as a common fracti…

Problem 17 Easy Difficulty

In $13-22,$ write each decimal as a common fraction.
$$
0 . \overline{108}
$$

Answer

$\frac{4}{37}$

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