# Express the value 100 using only the digit 9

• Nov 20th 2011, 01:19 PM
mmathh
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.
• Nov 20th 2011, 01:34 PM
Quacky
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?
• Nov 20th 2011, 01:45 PM
terrorsquid
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:

$\displaystyle (9+\frac{9}{9})*(9+\frac{9}{9})$
• Nov 20th 2011, 01:49 PM
SpringFan25
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
• Nov 20th 2011, 01:49 PM
skeeter
Re: 9s must appear alone
Quote:

Originally Posted by terrorsquid
$\displaystyle (9+\frac{9}{9})^2$

that method uses a 2 ...
• Nov 20th 2011, 02:43 PM
mmathh
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!
• Nov 20th 2011, 02:56 PM
Quacky
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?
• Nov 20th 2011, 03:12 PM
Deveno
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 (Clapping)

99.999999999999...... uses an infinite number to get the job done (does that count?)
• Nov 20th 2011, 04:06 PM
terrorsquid
Re: 9s must appear alone
Quote:

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 :D