# Express Using Fractions

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• Dec 3rd 2009, 05:12 PM
sologuitar
Express Using Fractions
Express the following repeating decimals as fractions.

(1) 13.513513...

(2) 52.31272727...
• Dec 3rd 2009, 05:26 PM
mr fantastic
Quote:

Originally Posted by sologuitar
Express the following repeating decimals as fractions.

(1) 13.513513...

(2) 52.31272727...

1) S = 13.513513 ... (A)

1000S = 13513.513 ... (B)

(B) - (A): ...... Now solve for S.

2) S = 52.31272727 .... (A)

100S = 5231.272727 .... (B)

10000S = 523127.2727 .... (C)

(C) - (B): .... Now solve for S.
• Dec 3rd 2009, 05:27 PM
VonNemo19
Quote:

Originally Posted by sologuitar
Express the following repeating decimals as fractions.

(1) 13.513513...

(2) 52.31272727...

Note that

$13.513513...=13+\frac{513}{1,000}+\frac{513}{1,000 ,000}+...$

the second problem is similar..
• Dec 3rd 2009, 08:16 PM
sologuitar
How???
Quote:

Originally Posted by mr fantastic
1) S = 13.513513 ... (A)

1000S = 13513.513 ... (B)

(B) - (A): ...... Now solve for S.

2) S = 52.31272727 .... (A)

100S = 5231.272727 .... (B)

10000S = 523127.2727 .... (C)

(C) - (B): .... Now solve for S.

I can do it now. However, where did S come from? What about this type of question indicated that subtraction was needed to find the answer?
• Dec 3rd 2009, 08:17 PM
sologuitar
Where???
Quote:

Originally Posted by VonNemo19
Note that

$13.513513...=13+\frac{513}{1,000}+\frac{513}{1,000 ,000}+...$

the second problem is similar..

Thanks for your reply but where are you going with the fractions?
• Dec 3rd 2009, 08:36 PM
mr fantastic
Quote:

Originally Posted by sologuitar
I can do it now. However, where did S come from? What about this type of question indicated that subtraction was needed to find the answer?

S is the symbol I used to represent the unknown fraction.

1) (B) - (A): 999S = 13500 => S = 13500/999 = 500/37.
• Dec 3rd 2009, 09:29 PM
sologuitar
Got it...
Quote:

Originally Posted by mr fantastic
S is the symbol I used to represent the unknown fraction.

1) (B) - (A): 999S = 13500 => S = 13500/999 = 500/37.

Thanks. I can use any variable other than S, right?
• Dec 3rd 2009, 09:30 PM
mr fantastic
Quote:

Originally Posted by sologuitar
Thanks. I can any variable other than S, right?

Yes. Use x if you like ....