PLEASE HELP!

I am studying for my MTSE exam 2015.

Can you please express $0.99999999...............$ in the form of fraction $(\frac{p}{q})$

#Algebra

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

How do you not know this? You are a level 5 in everything!!!!!

Krishna Ar - 7 years ago

Yes, how do you not know this? @ashwin korade

Sharky Kesa - 7 years ago

It is not the question you are thinking about. There are unlimited 9s and you have to present it in the form of fraction.

Example:- If there is $0.7777777777......$ , it would be represented as $\frac{7}{9}$ .

A Former Brilliant Member - 7 years ago

@A Former Brilliant Member – $\frac {1}{1}$ , if you let $\frac {1}{\infty}$ equal zero.

Sharky Kesa - 7 years ago

$0.99999999E = \frac {99999999E}{100000000}$ .

Sharky Kesa - 7 years ago

I'm just guessing, but I would say $\frac{11}{11}=\frac{10}{11} + \frac{1}{11} = 0.\overline{90} + 0.\overline{09} = 0.\overline{99}$ .

Mathematically, I don't see how this is different from any other fraction $\frac{p}{q}$ where $p=q$ , but I think this is more a question of "aesthetics". Please tell me why or why not this is correct, I'm here to learn!

Nicolas Bryenton - 6 years, 10 months ago

3/3

Radha Krishnan B - 7 years ago

As far as I know, 0,99999999... is equal to 0,(9)= (9-0) / 9 = 1 , so every fraction p/q with p=q expresses 0,9999... .

Adrian Stefan - 6 years, 11 months ago

let us say that E= 0.99999999....... so, 10E = 9.99999999......... now, 10E - E = 9.9999999999...... - 0.9999999999...... hence, 9E=9 E= 1 this means that any fraction in the form p/q with p = q would be equal to 0.9999999......

Sriram Venkatesan - 6 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$