Let a be the number of digits of 2^2001, and let b be the number of digits of 5^2001. Compute the sum of digits, a+b. (Hint: 2^5=32 which is 2 digits and 5^5=3125 which is 4 digits, therefore the sum of the digits is 6)
i bet you cant figure this out~!
2006-10-17 03:36:05 · 6 answers · asked by Anonymous in Education & Reference ➔ Homework Help
I always get counting wrong, but I got 2062.
Why would it ask such a boring problem? Why don't we bring back Hollerith cards for programming if we want to frustrate people?
2006-10-17 04:07:07 · answer #1 · answered by Bentley 4 · 0⤊ 0⤋
As a test, 2^2 = 4 and 5^2 = 25 and 25 + 4 = 29, but (2+5)^2 = 49 which means 2^2001 + 5^2001 does not equal (2+5)^2001. But given the huge exponent, one has a sense that the answer is similarly simple. Question: I'm unfamiliar with SAT, can you use a calculator. If so, then the answer is duck soup. Just calculate the answer, which the calculator will probably give in scientific notation. Take the number which the scientific notation gives as the number of places to move the decimal place to the right to get the full answer and add 1 for the one number which is to the left of the decimal place.
2006-10-17 04:25:10 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The answer is 2002
It's always one more than the power you are taking 2 and 5 to. The reason is the follows:
When you multiply a number with x digits and another number with y digits, the total will always have x+y digits.
So, to figure out total number of digits in 2^n and 5^n just multiply them to get 10^n which has n+1 digits (obviously).
Another way to look at it: To get the number of digits in a number, just take log(10, n) and round up. So, your problem can be restated as:
log(10, 2^n) + log(10, 5^n) =
n*log(10,2) + n*log(10,5) =
n*(log(10,2) + log(10,5)) =
n*(log(10, 2*5)) =
n*(log(10,10)) =
n * 1
the extra one gets you from the rounding up.
2006-10-17 04:39:28 · answer #3 · answered by Leo Z 2 · 0⤊ 0⤋
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2016-11-23 15:53:45 · answer #4 · answered by Anonymous · 0⤊ 0⤋
is it 2002?
2006-10-17 03:52:14 · answer #5 · answered by Amy 4 · 0⤊ 0⤋
2064
2006-10-17 04:00:57 · answer #6 · answered by Italian Mule 2 · 0⤊ 0⤋