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The decimal r = 2.666666 continues forever in that repeating
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Updated on: 20 Feb 2017, 10:04
Updated on: 20 Feb 2017, 10:04
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The decimal r = 2.666666 continues forever in that repeating decimal pattern. When written as a fraction in lowest terms, r = a/b, where a and b are positive numbers.
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Quantity A |
Quantity B |
a + b |
10 |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Originally posted by leonidbasin1 on 19 Feb 2017, 21:55.
Last edited by Carcass on 20 Feb 2017, 10:04, edited 1 time in total.
Last edited by Carcass on 20 Feb 2017, 10:04, edited 1 time in total.
Edited by Carcass
Re: The decimal r = 2.666666 continues forever in that repeating
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20 Feb 2017, 05:04
20 Feb 2017, 05:04
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Explanation
We have r = 2.666666......
So 10r = 26.666666....
We can write \(10r - r = 26.66666... - 2.666666.. = 24\)
So \(9r = 24\) or \(r =\frac{24}{9}=\frac{8}{3}\).
Hence a= 8 and b = 3. Thus \(a+b = 11\)
Hence clearly Quantity A is greater.
Alternatively you can remember .666666 .... is actually \(\frac{2}{3}\). So \(2.6666....\) is \(2\frac{2}{3}\).
The method above would work with any number of repeating decimals.
We have r = 2.666666......
So 10r = 26.666666....
We can write \(10r - r = 26.66666... - 2.666666.. = 24\)
So \(9r = 24\) or \(r =\frac{24}{9}=\frac{8}{3}\).
Hence a= 8 and b = 3. Thus \(a+b = 11\)
Hence clearly Quantity A is greater.
Alternatively you can remember .666666 .... is actually \(\frac{2}{3}\). So \(2.6666....\) is \(2\frac{2}{3}\).
The method above would work with any number of repeating decimals.
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Re: The decimal r = 2.666666 continues forever in that repeating
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26 May 2018, 10:16
26 May 2018, 10:16
6
leonidbasin1 wrote:
The decimal r = 2.666666 continues forever in that repeating decimal pattern. When written as a fraction in lowest terms, r = a/b, where a and b are positive numbers.
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Quantity A |
Quantity B |
a + b |
10 |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Given: r = 2.666666....
We know that 2/3 = 666666....
So, 2.666666.... = 2 + 2/3
Let's combine 2 + 2/3 into ONE fraction
2 + 2/3 = 6/3 + 2/3 = 8/3
Since the fraction 8/3 is in lowest terms, we can say that r = 2.666666... = 8/3 = a/b
So, a = 8 and b = 3
We get:
Quantity A: 8 + 3
Quantity B: 10
Evaluate:
Quantity A: 11
Quantity B: 10
Answer: A
Cheers,
Brent
