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24 May 2017, 13:13
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Convert 0.2512(12) to a fraction.
Source: GMAT Club Math Book v3 (pg 11)
Firstly, what does the number inside the parenthesis represent? Does it mean the recurrence goes on for 12 times?
Secondly, how I'd approach is :
- Extract the number until its first recurrence, so that'd be 2512.25122512 ...
- Subtract the original recurring number 0.25122512... from 2512.25122512....
- Resultant will be 2512
- Because we moved the decimal four spaces farther during our extract, I will divide 2512 by 9999
- = 2512/9999 = 0.251225122512 ...
What I did not understand is the approach from the Math book.
1. The number consisting with non-repeating digits and repeating digits is 2512;
2. Subtract 25 (non-repeating number) from above: 2512-25=2487;
3. Divide 2487 by 9900 (two 9's as there are two digits in 12 and 2 zeros as there are two digits in 25):
2487/9900=829/3300.
Am I on the same page with my approach? If yes, what's the difference between the two approaches?
Source: GMAT Club Math Book v3 (pg 11)
Firstly, what does the number inside the parenthesis represent? Does it mean the recurrence goes on for 12 times?
Secondly, how I'd approach is :
- Extract the number until its first recurrence, so that'd be 2512.25122512 ...
- Subtract the original recurring number 0.25122512... from 2512.25122512....
- Resultant will be 2512
- Because we moved the decimal four spaces farther during our extract, I will divide 2512 by 9999
- = 2512/9999 = 0.251225122512 ...
What I did not understand is the approach from the Math book.
1. The number consisting with non-repeating digits and repeating digits is 2512;
2. Subtract 25 (non-repeating number) from above: 2512-25=2487;
3. Divide 2487 by 9900 (two 9's as there are two digits in 12 and 2 zeros as there are two digits in 25):
2487/9900=829/3300.
Am I on the same page with my approach? If yes, what's the difference between the two approaches?
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