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Which of the following fractions will lead to a terminating decimal?

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Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

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New post 19 Jul 2019, 10:25
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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?  [#permalink]

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New post 19 Jul 2019, 10:33
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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?  [#permalink]

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New post Updated on: 19 Jul 2019, 23:41
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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. 83/80
Attachment:
83.PNG
83.PNG [ 5.51 KiB | Viewed 53 times ]


II. 23/120
Attachment:
230.PNG
230.PNG [ 8.25 KiB | Viewed 53 times ]


III. 33/480
Attachment:
33.PNG
33.PNG [ 6.63 KiB | Viewed 53 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 only

D. I and III only
E. I, II, and III

D is the answer. :heart
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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?  [#permalink]

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New post 19 Jul 2019, 12:20
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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?  [#permalink]

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New post 19 Jul 2019, 12:21
1
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?  [#permalink]

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New post 19 Jul 2019, 12:39
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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?  [#permalink]

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New post 19 Jul 2019, 12:51
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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 Non-Terminating 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?  [#permalink]

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New post 19 Jul 2019, 13:37
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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 non-terminating (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 non-terminating

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?  [#permalink]

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New post 19 Jul 2019, 14:26
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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?  [#permalink]

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New post 19 Jul 2019, 15:05
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Answer is D

Question 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 non-terminating 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 non-terminating.

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 non-terminating if it has any number other than 2 and 5 since 120 has 3 along with 2 and 5 the fraction will be Non-Terminating 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 non-terminating.
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?  [#permalink]

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New post 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?  [#permalink]

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New post 19 Jul 2019, 18:43
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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

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Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

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New post 19 Jul 2019, 20:21
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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 non-multiple 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?  [#permalink]

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New post 19 Jul 2019, 20:55
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Which of the following fractions will lead to a terminating decimal?

Fractions with numbers like 3, 7, 11 in the denominator will be non-terminating
I. 83/80 = 1.0375 Does not have 3,7,11 in the denominator

II. 23/120 = 0.1966666 Non-terminating

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?  [#permalink]

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New post 19 Jul 2019, 21:09
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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?  [#permalink]

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New post 19 Jul 2019, 21:18
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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?  [#permalink]

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New post 19 Jul 2019, 21:25
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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?  [#permalink]

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New post 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?  [#permalink]

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New post 19 Jul 2019, 21:33
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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?  [#permalink]

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New post 19 Jul 2019, 21:45
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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?   [#permalink] 19 Jul 2019, 21:45

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