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

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