0.9999999.....

Does 0.999999... has a fractional form ??? If it has , will you show please.. :(( Coz I always get 1 in solving it .. But it isnt equal to 1 right ??

Note by Noel Quirol
6 years, 3 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} $\boxed{123}$

Sort by:

It is equal to 1. Just like $0.00000... = 0$. :)

- 6 years, 3 months ago

i just dont get it..

- 6 years, 3 months ago

$100N = 99.9999.... \implies 99N = 99.999999... - 0.999999.....\implies 99N = 99 \implies N=1$

- 6 years, 2 months ago

yes, the fractional form is 1/1.....

- 6 years, 3 months ago

Thanks... :D

- 6 years, 3 months ago

Can you show me how did you get that 1/1.111111.. ?

- 6 years, 3 months ago

Find any number between $0.99999....$ and $1$. You can't! So they have to be equal!

- 6 years, 3 months ago

ohh , so thats it.. hehe :D Thanks..

- 6 years, 3 months ago