2020 AMC 10 B
Complete problem set with solutions and individual problem pages
The decimal representation of consists of a string of zeros after the decimal point, followed by a and then several more digits. How many zeros are in that initial string of zeros after the decimal point?(2020 AMC 10B, Question #12)
- A.
- B.
- C.
- D.
- E.
Solution 1:
Now we do some estimation. Notice that , which means that is a little more than . Multiplying it with , we get that the denominator is about . Notice that when we divide by an digit number, there are zeros before the first nonzero digit. This means that when we divide by the digit , there are integer decimal point.
Solution 2:
First rewrite as . Then, we know that when we write this in decimal form, there will be 40 digits after the decimal point. Therefore, we just have to find the number of digits in . and memming (alternatively use the fact that ), digits. Our answer is (D) 26
