consists of a string of zeros after the decimal point, followed by a 9 and then several more digits. How many zeros are in that initial string of zeros after the decimal point?
Answer Choices:
A. 23
B. 24
C. 25
D. 26
E. 27
Solution:
We have
20201=(10⋅2)201=1020⋅2201
Now we do some estimation. Notice that 220=10242, which means that 220 is a little more than 10002=1,000,000. Multiplying it with 1020, we get that the denominator is about
126 zeros 00…0
Notice that when we divide 1 by an n digit number as long as n is not a power of 10 , there are n−1 zeros before the first nonzero digit. This means that when we divide 1 by the 27-digit integer
126 zeros 00…0
there is (D)26 zeros in the initial string after the decimal point.