Problem Solving

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

Please explain.

kanha81 wrote: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

Please explain.

C b/c 10^n has n+1 digits
10^2 =100 has 2+1=3 digits. So
10^100 has 100+1 =101 digits.

dtweah wrote:

kanha81 wrote: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

Please explain.

C b/c 10^n has n+1 digits
10^2 =100 has 2+1=3 digits. So
10^100 has 100+1 =101 digits.

I am confused. The dtweah's logic is clear but the question is to express in [/u]decimal notation... that is like 0.1 or 2.3 ... i.e. decimal notation as i understand it... what dtweah has arrived at is the digits in the whole number no? pls someone explain... and whats OA?

thanks

ket wrote:

dtweah wrote:

kanha81 wrote: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

Please explain.

C b/c 10^n has n+1 digits
10^2 =100 has 2+1=3 digits. So
10^100 has 100+1 =101 digits.

I am confused. The dtweah's logic is clear but the question is to express in [/u]decimal notation... that is like 0.1 or 2.3 ... i.e. decimal notation as i understand it... what dtweah has arrived at is the digits in the whole number no? pls someone explain... and whats OA?

thanks

The question is what is the decimal form of a number? 25.5 25 3 are all decimal forms. Before every whole number there is a hidden decimal point. 100 is the same as 100.0 in decimal form. So the least decimal form for any number in exponent form is the write it out write it out. We don't include the decimal point if it is a whole number but do if it is a fractional number. I bet you would not want to write out 10^100 in its decimal form. Let's try.
1000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000.0

I thought I counted 100 zero's ( could have miscounted) plus the 1 should make 101 digits. This is the decimal representation of 10^100 and that is why 101 is the minimum digits for this representation. YOu are free to add as many zero's after the decimal point above but not before it.

thanks a lot Dtweah now i get your point.