Problem 6 · 1997 AJHSME
Medium
Fractions, Decimals & Percents
place-value
In the number 74982.1035, the value of the place occupied by the digit 9 is how many times as great as the value of the place occupied by the digit 3?
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Answer: C — 100,000.
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Hint 1 of 2
You don't need the actual place values (hundreds, thousandths) — just COUNT the gaps between the two digits. Each step to the left is one factor of 10.
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Hint 2 of 2
Moving one place left multiplies value by 10; so the ratio is just 10 raised to the number of places between the digits.
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Approach: count the place jumps, not the place values
- In 74982.1035, walk from the 3 leftward to the 9 and count steps: 3 → 0 → 1 → (decimal point) → 2 → 8 → 9. That's 5 places.
- Every step left multiplies the value by 10, so the 9's place is 10⁵ = 100,000 times the 3's place.
- Why this transfers: the digits in between (and what they are) never matter for a place-value ratio — only the number of place jumps does.
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