1998 AMC 8 Problem 5

Attempt Problem 5 of the 1998 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1998 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

5.

Which of the following numbers is largest?
9.123449.12344
9.1234‾9.123\overline{4}
9.1234‾9.12\overline{34}
9.1234‾9.1\overline{234}
9.1234‾9.\overline{1234}
Answer: B
Concepts:repeating decimalplace value
Small hint:
Write the repeating decimals out for a few places.
Big hint:
Compare at the first digit where the decimals differ.
Solution:
Each number starts with 9.1234.9.1234. The next digit is 44 for choices AA and B,B, 33 for C,C, 22 for D,D, and 11 for E.E.
Choice AA then terminates and is followed by zeros, while choice BB continues with more 44s. Thus, choice BB is largest.
Thus, the correct answer is B .
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