Problem 3 · 1991 AJHSME
Easy
Arithmetic & Operations
powers-of-ten
Two hundred thousand times two hundred thousand equals
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Answer: E — forty billion.
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Hint 1 of 3
Split each big number into a small front number and its trailing zeros. Two hundred thousand = 2 followed by how many zeros?
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Hint 2 of 3
Handle the fronts and the zeros separately: multiply the 2 × 2, then just pile ALL the zeros together.
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Hint 3 of 3
Five zeros from each factor means ten zeros stack up. What does 4 with ten zeros after it spell out?
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Approach: separate the front digits from the trailing zeros, then recombine
- Write each number as a front digit times its zeros: 200,000 = 2 with five 0's = 2 × 10⁵. Multiplying, the fronts give 2 × 2 = 4 and the zeros simply add up: 5 + 5 = 10 zeros.
- So the product is 4 followed by ten zeros = 40,000,000,000 = forty billion.
- Why this transfers: when multiplying round numbers, never line them up to multiply digit-by-digit — peel off the trailing zeros, multiply the small leftovers, and re-attach the combined zero count. (300 × 4000 = 12 with 5 zeros = 1,200,000.)
- Sanity check on the name: a billion has 9 zeros; 40 billion is 4 followed by 10 zeros, which is exactly what we got. ✓
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