Is my answer correct?

Question

Write 24.2422222... (with the last 2 repeating endlessly) as a fraction of integers.

(A) 10909/450

(B) 800/33

(C) 21818/999

(D) 12121/500

(E) None of these

I got (A) 10909/450. Is this the correct answer?

Answer 1

You mentioned that only the last "2" in the number was repeating, not the "24". So with this being the case, you have the correct answer. Well done!

The other person who responded understood that it was the 24 that was repeating. If that was the case, his answer would be correct.

Answer 2

24.24242424242....

let x=24.2424242424....

multiply both sides by 100 because 2 digits repeat (100=10^2)

100x=2424.24242424...

-

x= 24.24242424.....

_____________________

99x=2400 (notice that the decimal parts cancel each other)

x=2400/99

divide both terms by 3

x=800/33 which is (B)