Problem 3 · 1985 AJHSME
Easy
Fractions, Decimals & Percents
power-of-ten-arithmetic
10⁷ ⁄ (5 × 10⁴) =
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Answer: D — 200.
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Hint 1 of 2
Don't divide the messy numbers head-on. Split the bottom: handle the 10⁴ against the 10⁷ separately from the 5. Dividing powers of 10 just means cancelling matching zeros.
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Hint 2 of 2
Powers of ten divide by subtracting exponents: 10⁷ ⁄ 10⁴ = 10⁷⁻⁴ = 10³. Peel off the 10s first, deal with the small factor (the 5) last.
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Approach: subtract powers, then divide
- Group the tens: 10⁷ ⁄ 10⁴ = 10³ = 1000 (seven zeros over four zeros leaves three). Now just 1000 ÷ 5.
- 1000 ÷ 5 = 200.
- Sanity check: the answer should be a clean number with a few zeros, which immediately rules out the decimal choices (.002, .2) — peeling the powers of 10 first tells you the size before you ever divide.
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