What is the 99th digit after the decimal point in the decimal expansion of 5/12 + 7/15?

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Official Explanation

Official

To find the 99th digit after the decimal point in the decimal expansion of

\frac{5}{12} + \frac{7}{15}

, we first need a common denominator. The least common multiple of 12 and 15 is 60. Thus, we convert the fractions:

\frac{5}{12} = \frac{25}{60}

and…

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Comments

RheaJan 6, 2025

thanks for posting

LakshmiApr 2, 2025

thanksss

ApoorvJun 3

Is it just me or does finding the actual repeating pattern feel harder than the arithmetic? I got a repeating digit but want to make sure I'm reading the cycle right.

SrihitaJun 7

once you get the combined fraction, just do the division and watch which digit(s) start looping. the 99th position depends on where the loop sits.

ElleAug 24

thanks, this was helpful! love that it's not some insane calculation, just a clean repeating decimal.

YuktaMay 30

wait is the answer 3?? i think i messed up the position. does the repeating part start right after the decimal or is there a non-repeating digit first?

AshitaJun 9

that's exactly the trap — check whether every digit repeats or if the first one is separate. changes which digit lands in the 99th spot.

What this question tests

What it tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Common trap

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.