# Thread: Express the value 100 using only the digit 9

1. ## Express the value 100 using only the digit 9

Express 100 using only 9s , addition, subtraction, multiplication, division, exponents, and parentheses. The 9s must appear alone, that is, no multi digit numbers are allowed.
Thanks!
ignore question in title.

2. ## Re: 9s must appear alone

You can do this for any integer, just by having

$\displaystyle \frac{9}{9}+\frac{9}{9}+...$

Is there no other complication making this a challenge? Otherwise, $\displaystyle 9\times 9+9$ is already $\displaystyle 90$, and it isn't difficult to see how to proceed.

Are we only allowed to perform each operation once?

3. ## Re: 9s must appear alone

$\displaystyle (9+\frac{9}{9})^2$

edit: uses a 2, ignore :S...

Was trying to use operations only once, you can make it:

$\displaystyle (9+\frac{9}{9})*(9+\frac{9}{9})$

4. ## Re: 9s must appear alone

hopfully this doesn't count as trivial but:
$\displaystyle \frac{9}{9} + \frac{9}{9} +.... = 1+1+....$

repeat 100 times.

edit: didn't see previous identical reply

5. ## Re: 9s must appear alone

Originally Posted by terrorsquid
$\displaystyle (9+\frac{9}{9})^2$
that method uses a 2 ...

6. ## Re: 9s must appear alone

So don't need to use ALL of them? (9s, addition, subtraction, mult, division, exponents, AND parenthesis?... Thank you people!

7. ## Re: 9s must appear alone

We don't know - that was my original point. The question, as it stands, doesn't imply that you do. Is that the exact wording of the question?

8. ## Re: 9s must appear alone

$\displaystyle \left(\frac{9 \times 9}{9} \times \left(9 + \frac{9+9}{9}\right)\right) + \frac{9}{9}$

uses 9 9's

99.999999999999...... uses an infinite number to get the job done (does that count?)

9. ## Re: 9s must appear alone

Originally Posted by mmathh
So don't need to use ALL of them? (9s, addition, subtraction, mult, division, exponents, AND parenthesis?... Thank you people!
Using all of them:

$\displaystyle (9\times9)+(\frac{9+9+9+9}{9}\times 9) -(9+9)+(\frac{9}{9})^9$

Post #9