1969 AHSME Problems/Problem 20
Contents
Problem
Let equal the product of 3,659,893,456,789,325,678 and 342,973,489,379,256. The number of digits in is:
Solution 1
Through inspection, we see that the two digit number digits. Notice that any number that has the form multiplied by another will have its number of digits equal to the sum of the original numbers' digits.
In this case, we see that the first number has digits, and the second number has digits.
Note: this applies for numbers
Hence, the answer is digits
Solution 2
We can approximate the product with Now observe that , so we can further simplify the product with which means the product has digits.
-serpent_121
See also
1969 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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