Problem 1 · 1997 AJHSME
Easy
Fractions, Decimals & Percents
place-value
110 + 9100 + 91000 + 710000=
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Answer: C — 0.1997.
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Hint 1 of 2
Look at the denominators: 10, 100, 1000, 10000. Each fraction lives one place deeper in the decimal — the numerators are about to become the digits themselves.
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Hint 2 of 2
Powers-of-ten denominators ARE the decimal places: a number over 10ⁿ just drops its numerator into the nth decimal slot.
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Approach: read the digits straight off the place values
- Each denominator is a power of ten, so each numerator simply lands in its own decimal slot: 1/10 = 0.1 (tenths), 9/100 = 0.09 (hundredths), 9/1000 = 0.009 (thousandths), 7/10000 = 0.0007 (ten-thousandths).
- No carrying is needed because the digits never collide — they just stack into the answer: 0.1997.
- You'll see it again: any sum of numerators over 10, 100, 1000, … is really place-value in disguise. Reading the digits off beats long division.
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