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the rational equivalent

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by sanju09 » Thu Apr 07, 2011 1:58 am
What's the rational equivalent of the decimal 5.00351351351...?
(A) 198/37
(B) 188/37
(C) 1853/370
(D) 18513/3700
(E) 18503/3700


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by manpsingh87 » Thu Apr 07, 2011 2:32 am
sanju09 wrote:What's the rational equivalent of the decimal 5.00351351351...?
(A) 198/37
(B) 188/37
(C) 1853/370
(D) 18513/3700
(E) 18503/3700


Made up
5.00351351351.... first of all forget about the 5.00 part just concentrate on .351351..
since its a recurring series of 351 therefore its fractional equivalent=351/999=13/37
now divide 13/37 by 100 and add 5 into it, therefore we have 5+13/3700=18513/3700 hence D
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by sanju09 » Thu Apr 07, 2011 2:54 am
manpsingh87 wrote:
sanju09 wrote:What's the rational equivalent of the decimal 5.00351351351...?
(A) 198/37
(B) 188/37
(C) 1853/370
(D) 18513/3700
(E) 18503/3700


Made up
5.00351351351.... first of all forget about the 5.00 part just concentrate on .351351..
since its a recurring series of 351 therefore its fractional equivalent=351/999=13/37
now divide 13/37 by 100 and add 5 into it, therefore we have 5+13/3700=18513/3700 hence D
Good, it's same as this


5.00351351351... = 5 + 0.00351351351...

= 5 + 1/100 × (0.351351351...)

= 5 + 1/100 × (351/999)

= 5 + 1/100 × (13/37)

= 5 + 13/3700

= [spoiler]18513/3700


D[/spoiler]
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by 6983manish » Thu Apr 07, 2011 2:56 am
manpsingh87 wrote:
sanju09 wrote:What's the rational equivalent of the decimal 5.00351351351...?
(A) 198/37
(B) 188/37
(C) 1853/370
(D) 18513/3700
(E) 18503/3700


Made up
5.00351351351.... first of all forget about the 5.00 part just concentrate on .351351..
since its a recurring series of 351 therefore its fractional equivalent=351/999=13/37
now divide 13/37 by 100 and add 5 into it, therefore we have 5+13/3700=18513/3700 hence D
Thanks manpsingh87 and Sanju.

Pretty simple approach to this tricky question.
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by Brent@GMATPrepNow » Thu Apr 07, 2011 9:34 am
For anyone wondering how the above people recognized that 0.351351351... = 351/999, here's the rationale

First let's let the fraction F equal 0.351351351351...

So, F = 0.351351351351...
This means 1000F = 351.351351351351...

Note: I multiplied F by 1000 so that F and 1000F would both have the EXACT SAME numbers to the right of the decimal place.

Now notice what happens when we subtract 1000F - F

We get 1000F - F = 351.351351351351... - 0.351351351351...
Next, simplify: 999F = 351
Finally, divide both sides by 999 to get F = 351/999
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by force5 » Thu Apr 07, 2011 11:44 am
good one..
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