1989 AMC 8 Problem 3

Attempt Problem 3 of the 1989 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 1989 AMC 8 solutions, or check the answer key.

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

3.

Which of the following numbers is the largest?
0.990.99
0.90990.9099
0.90.9
0.9090.909
0.90090.9009
Answer: A
Concepts:decimalplace value
Small hint:
Give every number the same number of decimal places by appending zeros
Big hint:
Compare digit by digit from the left; the hundredths place decides between the leading 0.90.9 numbers
Solution:
Write each number with four decimal places: 0.9900,0.9900, 0.9099,0.9099, 0.9000,0.9000, 0.9090,0.9090, 0.9009.0.9009.
Comparing from the left, 0.99000.9900 has the largest hundredths digit, so 0.990.99 is the largest.
Thus, the correct answer is A .
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