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
the rational equivalent
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- sanju09
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- manpsingh87
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5.00351351351.... first of all forget about the 5.00 part just concentrate on .351351..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
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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- sanju09
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Good, it's same as thismanpsingh87 wrote:5.00351351351.... first of all forget about the 5.00 part just concentrate on .351351..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
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
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]
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
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Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
- 6983manish
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Thanks manpsingh87 and Sanju.manpsingh87 wrote:5.00351351351.... first of all forget about the 5.00 part just concentrate on .351351..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
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
Pretty simple approach to this tricky question.
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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
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