Problem 2 · 1990 AJHSME
Easy
Fractions, Decimals & Percents
place-value
Which digit of .12345, when changed to 9, gives the largest number?
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Answer: A — the 1.
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Hint 1 of 2
You only get to bump ONE digit up to 9. Where would that extra jump add the most — near the front of the decimal, or near the back?
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Hint 2 of 2
The leftmost decimal digit is the tenths place, worth the most. The same place-value idea as making big/small numbers: changes near the front matter most.
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Approach: spend your one change on the most valuable place
- Reading left to right, the places shrink fast: tenths, hundredths, thousandths… A digit's *position* decides how much changing it helps, not the digit itself.
- The leftmost digit (the 1) sits in the tenths place — the most valuable spot. Bumping it to 9 turns .12345 into .92345, a jump of 0.8.
- Changing any digit further right adds far less (the 2 only buys 0.07). So change the 1.
- *Sanity check:* .92345 clearly beats .19345, .12945, etc. — the leading digit dominates, exactly like why 9xxx beats x9xx in whole numbers.
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