GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Aug 2020, 13:24 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # What is the least number of digits (including repetitions) needed to e

Author Message
TAGS:

### Hide Tags

Intern  Joined: 08 Aug 2009
Posts: 17
What is the least number of digits (including repetitions) needed to e  [#permalink]

### Show Tags

1
8 00:00

Difficulty:   15% (low)

Question Stats: 72% (00:59) correct 28% (01:09) wrong based on 177 sessions

### HideShow timer Statistics

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
Intern  Joined: 31 Oct 2009
Posts: 22
Re: What is the least number of digits (including repetitions) needed to e  [#permalink]

### Show Tags

8
1
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:
$$10^{100}=101 digits$$
##### General Discussion
Manager  Joined: 19 Nov 2007
Posts: 114
Re: What is the least number of digits (including repetitions) needed to e  [#permalink]

### Show Tags

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
Intern  Joined: 11 Nov 2009
Posts: 7
Re: What is the least number of digits (including repetitions) needed to e  [#permalink]

### Show Tags

1
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.
Retired Moderator Joined: 02 Sep 2010
Posts: 701
Location: London

### Show Tags

rtaha2412 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

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)
_________________
Manager  Joined: 09 Jun 2010
Posts: 90

### Show Tags

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
Manager  Status: Not afraid of failures, disappointments, and falls.
Joined: 20 Jan 2010
Posts: 241
Concentration: Technology, Entrepreneurship
WE: Operations (Telecommunications)

### Show Tags

1
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 $$100 + 1 = 101$$

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 $$1$$
==> $$100+1=101$$
Intern  Joined: 25 Aug 2010
Posts: 49

### Show Tags

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
Manager  Joined: 09 Jun 2010
Posts: 90

### Show Tags

1
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.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10780
Location: Pune, India
Re: What is the least number of digits (including repetitions) needed to e  [#permalink]

### Show Tags

2
wolver123 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

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.
_________________
Karishma
Veritas Prep GMAT Instructor

Intern  Joined: 28 Sep 2016
Posts: 1
What is the least number of digits (including repetitions) needed to e  [#permalink]

### Show Tags

10^(-1)×10^101= 10^100
Can also be written in decimal notation as 0.1×10^101 = 10^100
Non-Human User Joined: 09 Sep 2013
Posts: 15596
Re: What is the least number of digits (including repetitions) needed to e  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: What is the least number of digits (including repetitions) needed to e   [#permalink] 26 Jul 2019, 05:58

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