The least number of digits (including repetitions) needed to express 10^100 in decimal notation GMAT Problem Solving

Question: What is the least number of digits (including repetitions) needed to express 10^100 in decimal notation? GMAT Problem Solving 

a) 4
b) 100
c) 101
d) 1000
e)1001

“What is the least number of digits (including repetitions) needed to express 10^100 in decimal notation?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation: 

Approach Solution 1:

We are asked to find out the least number of digits (including repetitions) needed to express 10^100 in decimal notation. We will check the decimal notations for each, starting from 10^2.

For 10^2, it is followed by 2 zeroes in decimal notation

For 10^3, it is followed by 3 zeroes in decimal notation

For 10^4, it is followed by 4 zeroes in decimal notation

In similar ways, if we calculate, we get:

10^100 is followed by 100 zeroes in decimal notation.

So to calculate the number of digits :

1 + 100 zeroes
=>101

Correct Answer: C 

Approach Solution 2:

We are asked to find out the least number of digits (including repetitions) needed to express 10^100 in decimal notation. We will check the decimal notations for each by considering “n”.

Let us consider 10^n, where n is 1,2,3,4……

So we get 10^2=100, which is 3 digits
We also get 10^3=1000, which is 4 digits…. And so on.

Hence, to calculate number of digits:
10^n = n+1
So by following this formula, we get:
10^100 = 100+1
Hence, the answer is 101.

Correct Answer: C 

Approach Solution 3:

Decimal notation is the writing of numbers in a base-10 numeral system. It derives its name from Deci = 10
For example:

55 = 10X5 + 5;

123 = (10^2)X1+(10^1)X2+(10^0)X3

This is the general numeric system used for expressing numbers.

Hence, 10^(-1)×10^101= 10^100

Can also be written in decimal notation as 0.1×10^101 = 10^100.    

Correct Answer: C 

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