1. ## Express Using Fractions

Express the following repeating decimals as fractions.

(1) 13.513513...

(2) 52.31272727...

2. 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.

3. 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..

4. ## How???

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?

5. ## Where???

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?

6. 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.

7. ## Got it...

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?

8. Originally Posted by sologuitar
Thanks. I can any variable other than S, right?
Yes. Use x if you like ....