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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 10:25
Which of the following fractions will lead to a terminating decimal?
I. \(\frac{83}{80}\)
II. \(\frac{23}{120}\)
III. \(\frac{33}{480}\)
To find out if a fraction is terminating or not, we would have to look at the denominator it has to be in the \((2^n)(5^m)\) form ( where n and m are non negative)
i) \(80 = 2*2*2*2*5 =(2^4)(5^1)\)
II) 120 = 4*10*3*10 => since 3 is found in the denominator, this fraction will be non terminating.
III) reducing the fraction = \(\frac{33}{480}\) = \(\frac{11}{160}\)
=>\(160 = 2*2*2*2*(2*5)= 2^5*5^1\)
Answer: D.



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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 10:33
If the denominator of the fraction, in its reduced form, contains no other prime number facors other than 2 and 5, then the fraction is terminating.
I) \(\frac{83}{80}\)= \(\frac{83}{2^4*5}\) Denominator contains only 2 and 5 as prime factors, hence \(\frac{83}{80}\) leads to terminating decimal.
II) \(\frac{23}{120}\)= \(\frac{23}{2^3*3*5}\) Denominator contains 2, 3 and 5 as prime factors, hence \(\frac{23}{120}\) does not lead to terminating decimal.
III)\(\frac{33}{480}\)= \(\frac{3*11}{2^5*3*5}\)=\(\frac{11}{2^5*5}\) Denominator contains only 2 and 5 as prime factors, hence \(\frac{33}{480}\) leads terminating decimal.
IMO D



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Which of the following fractions will lead to a terminating decimal?
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Updated on: 19 Jul 2019, 23:41
Which of the following fractions will lead to a terminating decimal?We just simply need to perform division calculations, and see do we have a terminating decimal or not: I. 83/80Attachment:
83.PNG [ 5.51 KiB  Viewed 56 times ]
II. 23/120Attachment:
230.PNG [ 8.25 KiB  Viewed 56 times ]
III. 33/480Attachment:
33.PNG [ 6.63 KiB  Viewed 56 times ]
If we will test by concept then:Number will have finite number of integers after decimal of denominator consists of only 2, 5 or both. I. Has both 2 and 5, so it will terminate II. Has 2 and 5, but also 3, will not terminate III. Has only 2 and 5, thus will terminate A. None B. I only C. I and II onlyD. I and III onlyE. I, II, and IIID is the answer.
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Last edited by GKomoku on 19 Jul 2019, 23:41, edited 1 time in total.



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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 12:20
Terminating decimal is the prime factor of the denominator of a fraction, and it contains only 2 and 5 or both. I. 83/80>80=(2^4)*5>83/((2^4)*5>Correct
II. 23/120>120 =(2^3)*3*5>It has 3 in the denominator>Incorrect
III. 33/480>480 =(2^5)*3*5>33/((2^5)*3*5)>11/((2^5)*5)>Correct >Only I & III



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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 12:21
Quote: Which of the following fractions will lead to a terminating decimal?
I. \(\frac{83}{80}\)
II. \(\frac{23}{120}\)
III. \(\frac{33}{480}\)
A. None B. I only C. I and II only D. I and III only E. I, II, and III
1. for simplicity we can check 83/ 8 =10.3741 hence terminating 2. 23/ 12 = 1.8166666 hence non terminating 3. 33/48 = \(\frac{33}{(4*12)}\) 33/4= 8.25 8.25/12 . is also terminating. Hence 1 and 3 Option D



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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 12:39
Which of the following fractions will lead to a terminating decimal?
A little time consuming process of diving the number and solving till the decimal terminates. Since denominators are small and easy numbers, can be done under 2 min.
I. \(\frac{83}{80}\) 83/80 = 1.0375 > Terminating decimal.
II. \(\frac{23}{120}\) 23/120 = 0.191666... > Non terminating decimal.
III. \(\frac{33}{480}\) 33/480 = 11/160 = 0.06875 > terminating decimal.
Hence, fractions I and III lead to terminating decimal.
A. None B. I only C. I and II only D. I and III only E. I, II, and III
Answer Choice: D



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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 12:51
If a fraction contains just the powers of 2 and 5 in the denominator, it will definitely be a terminating decimal. With this lets check the given fractions, I. \(\frac{83}{80}\); Denominator is \(2^{4}*5\) > Terminating Decimal II. \(\frac{23}{120}\); Denominator is \(2^{3}*5*3\) > Since it contains 3, Its a NonTerminating Decimal III.\(\frac{33}{480}\);Upon reduction \(\frac{1}{160}\); Denominator is \(2^{5}*5\) > Terminating Decimal Ans :D
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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 13:37
Which of the following fractions will lead to a terminating decimal?
I. 83/80
II. 23/120
III. 33/480
A. None B. I only C. I and II only D. I and III only E. I, II, and III
All we need to remember about termination decimals are two simple rules: 1) the decimal is terminating if there is an integer 2, integer 5 or both in the denominator. 2) if there are any other prime factors in denominator, then the decimal is nonterminating (recurring)
so let's look through the given fractions:
1. 83/80 80 = (2^4)* 5 the the decimal is terminating
2. 23/120
120 = (2^3)*3*5 the the decimal is nonterminating
3. 33/480
480 =(2^5)*3*5 the decimal is terminating, because there is an integer 3 in numerator. So 3 in denominator is eliminated.
The answer is D



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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 14:26
Note: If the denominator of the fraction consists of only \(2^{x}*5^{y}\), then we will have a terminating decimal. 1. \(\frac{83}{80}\) Since the denominator is \(2^{4}*5\), yes terminating. 2. \(\frac{23}{120}\) Since the denominator is \(2^{3}*3*5\), not terminating. 3. \(\frac{33}{480}\) Since the denominator is \(2^{5}*5\), yes terminating. Both \(1\) and \(3\) are terminating decimals. Hence D
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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 15:05
Answer is DQuestion is asking which of the following fractions will lead to a terminating decimal? I. 83/80 II. 23/120 III. 33/480 In order to know whether any fraction is terminating or nonterminating we just need to consider the denominator only and we need to see that whether the denominator contains only 2, 5 or both. If the denominator contains any number other than 2 or 5 then the fraction will be nonterminating. I. 83/80 We can express 80 as 2^4 * 5. Since 80 has only 2 and 5 therefore the fraction is Terminating Decimal. II. 23/120 We can express 120 as 2^3 * 3 * 5. We know that a fraction will be nonterminating if it has any number other than 2 and 5 since 120 has 3 along with 2 and 5 the fraction will be NonTerminating Decimal. III. 33/480 = 11/160. In its simplest form the fraction has 160 as its denominator now we need to see whether the fraction is terminating or nonterminating. We can express 160 as 2^5 * 5. Since 160 has only 2 and 5 therefore the fraction is Terminating Decimal. Answer is D
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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 15:15
Which of the following fractions will lead to a terminating decimal?
Will terminate when the prime factorization of the denominator of the fraction has only prime factors of 2 and/or 5
I.83/80 =83/(2^4•5) will terminate
II. 23/120 =23/(2^3•3•5) has 3 as one of factors so Nope!
III. 33/480= 33/(2^5•3•5) has 3 as one of factors so Nope!
A. None B. I only C. I and II only D. I and III only E. I, II, and III
Answer B
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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 18:43
Which of the following fractions will lead to a terminating decimal? I. 83/80 If we divide 3 by 8 then we get terminating decimal II. 23/120 If we divide 23 by 12 then we get 6 digit repetitive. So this is not terminating. III. 33/480 If we divide 11 by 16 then we get terminating decimal. Answer: I and III D Posted from my mobile device
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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 20:21
I. 83/80 = 83/(2^4*5) If the denominator has 2 or 5 or higher powers of 2 or 5. It will always be terminating decimal > Terminating
II. 23/120 = 23/(2^3*3*5) Since the denominator has a multiple of 3 & numberator a nonmultiple of 3, it will always be a recurring decimal > Non terminating
III. 33/480 = 33/2^5*3*5 = 11/2^5*5 If the denominator has 2 or 5 or higher powers of 2 or 5. It will always be terminating decimal > Terminating
IMO Option D
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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 20:55
Which of the following fractions will lead to a terminating decimal? Fractions with numbers like 3, 7, 11 in the denominator will be nonterminating I. 83/80 = 1.0375 Does not have 3,7,11 in the denominator II. 23/120 = 0.1966666 Nonterminating III. 33/480 = 11/160 = 0.06875 Terminating Option D  I and III
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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 21:09
for no to be terminating decimal it should have 2*5 as no in denominator out of given options option i & iii are terminating decimals 83/80 ; 80 = 2^4*5^1 yes 23/120 ; 120 ; 2^3*3^1*5^1 ; no 33/480 ; 480 ; 2^5*3^1*5^1 ; yes IMO D Which of the following fractions will lead to a terminating decimal? I. 83808380 II. 2312023120 III. 3348033480 A. None B. I only C. I and II only D. I and III only E. I, II, and III
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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 21:18
In order for a fraction to be a terminating decimal, denominator needs to be in the form of 2^x * 5^ when fraction is reduced.
I) 83/80 = 83/(16*5) = 83/(2^4*5)  Terminating II) 23/120 = 23/(3*40) = 23/(3*2^3*5)  Not terminating III) 33/480 = 11/160 = 11/(2^4*10) = 11/(2^5*5)  Terminating
Answer is D



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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 21:25
Terminating Decimal  All the integer divided by any integer power of 2 or 5 gives terminating decimal.
1st statement  Denominator = 80 80 = 2^4.5
Hence statement 1 is terminating decimal.
2  simplified form is 23/120 We have 3 in the denominator, number 3 will give recurring decimal
3  33/480 > 11/160
The denominator is a factor or 2 and 5 only hence terminating.
So Statement 1 and 3 are terminating decimal
Hence, D is the Answer.



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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 21:26
Which of the following fractions will lead to a terminating decimal?
As the given 3 fractions have common factors in denominator its easier to multiply each fraction by 40 and reduce the denominator
\(\frac{83}{80}*40 = \frac{83}{2}\)
\(\frac{23}{120}*40 = \frac{23}{3}\)
\(\frac{33}{480}*40 = \frac{33}{12}\)
this division is easier to tackle than larger denominators. Only \(\frac{83}{2}\) leads to terminating decimal
B is the answer!



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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 21:33
A number will terminate if its denominator consists of only 2's, 5's or both. Let's check denominators of the following fractions:
I. \(\frac{83}{80}\)=\(\frac{83}{2^4*5^1}\)  will terminate because denominator has 2's and 5's only
II. \(\frac{23}{120}\)=\(\frac{23}{2^3*5^1*3^1}\)  will not terminate because denominator has 3
III. \(\frac{33}{480}\)=\(\frac{11}{2^5*5^1}\) will terminate because denominator has 2's and 5's only.
As we saw above, only I and III work, answer is D



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Re: Which of the following fractions will lead to a terminating decimal?
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19 Jul 2019, 21:45
For a fraction to be a terminating decimal, the denominator must only have 2s and 5s as factor. A) 83/80 80 = 2^4 * 5 Hence, this is terminating B) 23/120 120 = 2^3 * 3 * 5 As the denominator has 3 as a factor, this is not terminating. C) 33/480 33 = 3 * 11 480 = 2^5 * 3 * 5 Simplifying, it becomes 11/160, which is terminating Hence, I and III are terminating.
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Re: Which of the following fractions will lead to a terminating decimal?
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