What is the least number of digits (including repetitions) needed to

Question

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

(A) 4
(B) 100
(C) 101
(D) 1000
(E) 1001

jeckll · Accepted Answer

This can easily be solved by looking at patterns of 10:

10^1=2 digits 
 10^2=3 digits 
 10^3=4 digits 
 10^4=5 digits 
...so...
 10^n=n+1 digits

thus:
 10^{100}=101 digits

jade3 · Answer

10^n is a decimal number with a 1 followed by n zeros.
So 10^100 will include 100 0's + 1 digit for 1 = 101
So the answer is C.

gmatter10 · Answer

10^2 is 1 followed by 2 zeroes in decimal notation

10^3 is 1 followed by 3 zeroes in decimal notation

10^4 is 1 followed by 4 zeroes in decimal notation

Hence 10^100 is 1 followed by 100 zeroes in decimal notation

Number of digits is 1 + 100 zeroes and hence answer C.

shrouded1 · Answer

I have corrected the question. It should say  10^{100}

This number is 1 followed by 100 zeroes, so you have 101 digits in all, hence the answer (c)

soumanag · Answer

Consider  10^n , n being 1, 2, 3 ........

10^2  = 100 => 3 digits
 10^3  = 1000 => 4 digits .... so on

number of digits for  10^n  = n+1

10^100 => number of digits = 100+1 = 101

Correct option C

AtifS · Answer

Answer: C
Explanation: 
The number of digits (least) for  10^n = (n+1)  Where,  n \geq 0 .

So, The number of digits (least) for  10^{100}  are  100 + 1 = 101 
Thus the answer is C.

Or, you can see that there are one hundred  0's  followed by  1  (to the right of  1 ) and the least number of digits would be number of  0's  plus  1  
==>  100+1=101

vitamingmat · Answer

C is the ans

10^2 = 100
10^3 =1 000
10^4 = 1 0000
so 10 ^100 willm be having 1 hunderd zeros = total digits = 1+ 100 = 101

soumanag · Answer

Hi utin, Decimal notation is the writing of numbers in a base-10 numeral system. It derives its name from Deci = 10 I guess

examples = 55 = 10X5 + 5; 123 = (10^2)X1+(10^1)X2+(10^0)X3 This is the general numeric system used for expressing numbers.

KarishmaB · Answer

I am guessing what put you off the question was "in decimal notation". It just means using the decimal system of counting (with 10 digits 0 - 9) as opposed to other systems such as binary (using only two digits 0 and 1) etc. Decimal notation is the usual system we use to write numbers. It has nothing to do with the decimal point.

Upamanyu15 · Answer

10^(-1)×10^101= 10^100
Can also be written in decimal notation as 0.1×10^101 = 10^100
The answer is C

MathRevolution · Answer

10^{100} = 1 followed by 100 zeroes: Total 101 digits.

Answer C

tryorcry · Answer

Lesson learned :
7 * 10^5 is NOT a decimal notation but a scientific notation
700000 is a decimal notation

Similarly 10 with added zeroes will be a decimal notation with base 10.
Answer C

What is the least number of digits (including repetitions) needed to

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is the least number of digits (including repetitions) needed to

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards