decimal notation

[hakyology]

What is the least number of digits (including repetitions) needed to express 10^100 in decimal notation?
A)4
B)100
C)101
D)1,000
E)1,001


Please explain.

The answer is C.

Thank you.

[sethids]

10^100 means writing 1 followed by 100 zeroes.
Hence 101 digits are required to represent it in decimal notation.

[dalwow]

Another way to think about it is this....imagine you have 100 10's lined up to multiply by each other. Multiply the first 2 and you get 100 which is 3 digits. Now you know that each additional 10 will add one more digit. You have 98 more 10's, so you take the 3 digits you already have and add the 98 additional digits and you get 101.

[lightbulb]

10^1 = 10 Use 2 digits (1 + 1)
10^2 = 100 Use 3 digits (2 + 1)
10^3 = 1000 Use 4 digits (3 + 1)

=> 10^n would require n+1 digits