Problem 3 · 1997 AJHSME
Easy
Fractions, Decimals & Percents
compare-decimals
Which of the following numbers is the largest?
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Answer: B — 0.979.
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Hint 1 of 2
Don't judge by how many digits a decimal has — 0.9709 is not bigger just because it's longer. Compare left to right, one place at a time.
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Hint 2 of 2
Decimals compare like a race: the first place where they differ decides the winner, and everything after that is irrelevant.
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Approach: left-to-right place comparison
- Tenths first: all five start 0.9…, a tie. Move right.
- Hundredths: 0.97, 0.979, 0.9709 all have a 7, but 0.907 has 0 and 0.9089 has 0 — those two are knocked out, even though 0.9089 has lots of digits.
- Thousandths decides the survivors: 0.979 has a 9 while 0.97 and 0.9709 have 0, so 0.979 wins.
- Why this transfers: extra trailing digits never make a decimal bigger — only an earlier place can. 0.97 = 0.9700, which already beats 0.9709? No: 0.9700 vs 0.9709 ties through hundredths, then 0 vs 0 in thousandths, then 0 vs 9 — so 0.9709 > 0.97. The first difference rules.
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