Discussion
The value of 0.12343434… is:
Answer: A
The value is 611/4950. Let x = 0.12343434... Then 10000x = 1234.3434... and 100x = 12.3434..., and subtracting gives 9900x = 1222, so x = 1222/9900 = 611/4950. The fraction 611/9900 is half of that value, 1222/9999 would repeat the block 1222, and the bare 9900 printed in the third option is not a fraction of that value. Another way to see it: subtract the non-repeating part. The number is 0.12 followed by the repeating block 34. With x = 0.12343434..., 100x = 12.343434... and 10000x = 1234.343434..., so the repeating tail cancels when the first is subtracted from the second, leaving 9900x = 1222.
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