Number of 0's in the Number of 0's

Number Theory Level 2

Let $N$ be the number of 0's needed to write out $10^{100000}$ .

How many 0's are needed to write out the number $N$ ?

The answer is 5.

8 solutions

Andrew Ellinor
Sep 28, 2015

The number $10^n$ requires $n$ 0's to fully write out. This means $10^{100000}$ requires 100000 0's to write out and we see that 5 0's are needed to write out 100000.

i wrote that and was taked as wrong

Cuauhtemoc Chacon - 5 years, 8 months ago

How do you get 5? 10 raised to the 100000th power is written out 1 followed by 100000 zeros. Just as 10 raised to the second power is 100 (2 zeros) and 10 raised to the third power is 1000(3 zeros), 10 raised to the 100000th power requires 100000 zeros.

Adam Folk - 5 years, 4 months ago

I think the question needs a little more work and re-writting. The question is: How many 0's are needed to write out the number N? It doesn't matter if N is 5 or 6. You need "ZERO 0's" to write either 5 or 6, so the answer should be 0. It's only obvious.

Fábio Casado - 5 years, 8 months ago

N is 100000

Zain Majumder - 2 years, 9 months ago

N is the number of 0's needed to write out 10^100000. So, N=100000 zeroes needed to write out 10^100000. The question is how many zeroes needed to write out N=100000? The answer to which is 5. So 0 would be the wrong answer.

Saurav Deb Purkayastha - 5 years, 8 months ago

The hard thing in the question is you have to read the question carefully...

Kitniti Witchayapaisitsakul - 4 years, 12 months ago

This question is dumb. Enjoy your "win."

chris applegate - 4 years, 9 months ago

It should be 6 right. 5 zeroes in 100000 and 1 zero in the 10

Nonymous H - 1 year, 8 months ago

I don't think this question is mathematical in nature. I could ask how many 1's does it take to right out 1^11111111? Is it only 1 or 9? This is just a trick, in semantics really, not a math problem.

Robert Vasquez - 7 months, 1 week ago

Victor Duarte da Silva
Sep 28, 2015

There are a lot of ways to write the same number.

e.g: $10^{100000}$ can be write as $10^{10^5}$ that needs 2 0's to be write, and so, no zeros is needed. Or write in another base, that gives another answer, or insert zeros in the left of any number to justify whatever have you answered. The only way got the wrong result is answering with a non natural number.

Please, write the question a little more formal.

Pretty sure a level 2 question wouldn't have you changing bases. And adding zeros to the left of a number? When is it that ever really a necessary thing?

Why would you try the more elaborate answers before the simpler one? (occam's razor is usually a pretty good thing to keep in mind).

Though I can see the merit in adding something like "N is the number of 0's when 10^100000 is written with no exponents"

A Former Brilliant Member - 5 years, 8 months ago

Tarun Prasad Sahu
Sep 28, 2015

$10^{100000}$ has $100000$ zeroes in it. So $N=100000$ . Number of zeroes in $N$ is $5$ .

Except that the question asks how many zeroes to write N......If N=5 then I don't need ANY zeroes to write N.

Allie Arnold - 5 years, 8 months ago

Allie, according to your logic,

If the same question was asked with 10^10 instead of 10^100000;

you will say N = 1 because in 10^10, power of 10 is 10 and it has only one zero. So number of zeroes to write N = 0.

Whereas I will say 10^10=10000000000. So N = 10. Number of zeroes needed to write N = 1.

Tarun Prasad Sahu - 5 years, 8 months ago

John McLachlan
Nov 30, 2017

Makes me wonder why they invented scientific notation ;) I was happy to get that one right

Mohammad Khaza
May 17, 2017

10^1=10. HERE IS ONE 0.

10^2=100.HERE IS TWO 0.

10^3=1000.HERE IS THREE 0.

THEN DEFINITELY 10^5 OR 10^00000 HAS FIVE ZEROES.

SO,THE ANSWER IS 5

very nice explanation

Halima Tahmina - 4 years ago

There is clearly a problem with language here. The question CLEARLY asks how many zeros are required to write out the NUMBER, NOT the expression, so 100,000 zeros, or actually 100001 zeros, is the correct answer. FIVE is simply rewriting the expression, not the number. PLEASE, no trick questions here, okay?

Robert Cormia - 2 years, 3 months ago

thanks.your comment inspired me

Mohammad Khaza - 4 years ago

Ashish Menon
Nov 28, 2015

10 raised to 100000 requires 100000 0's. And 100000 has 5 zeroes. So the answer is 5.

Devansh Shah
Oct 18, 2015

No of digits in any number is equal to the log of that no to the base10. Hence log10^100000= 100000 which is N. So no of zeroes required to write N is 5

David Jimenez
Sep 28, 2015

the better answer is one. namely 10^5. since we're using scientific notation from the start.

Number of 0's in the Number of 0's

The answer is 5.

8 solutions

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