1997 AMC 8 Problem 6

Attempt Problem 6 of the 1997 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1997 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

6.

In the number 74982.103574982.1035 the value of the place occupied by the digit 99 is how many times as great as the value of the place occupied by the digit 3?3?
1,0001{,}000
10,00010{,}000
100,000100{,}000
1,000,0001{,}000{,}000
10,000,00010{,}000{,}000
Answer: C
Concepts:place valueexponent
Small hint:
Each step left in place value multiplies by 1010
Big hint:
Compare the place values occupied by 99 and 33
Solution:
Note that each digit has ten times the value of the digit to its right.
The place occupied by 99 is 55 spaces to the left of the place occupied by 3.3.
This means that it is 105=100,000 10^5 = 100,000 times as great.
Thus, C is the correct answer.
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