×

# How did you know that?

To all those experienced students with decimals and fractions, we know that 0.33333... is 1/3 because only the 3 is repeating, so you simply put one 9 in the denominator to get 3/9 or 1/3. Or perhaps... 0.63 repeating can be expressed as 63/99 since two digits are being repeated to get 7/11. (if you didn't know this before hand, it's fine. Now you know :D). A harder question may ask 0.1256, where only 56 part is being repeated. This may be changed to 0.12+56/9900. Yes, there is a pattern, but I want to challenge you to derive this algebraically(use examples if it helps) BONUS: Turn 0.166666.. and 0.2118118118118.... into fractional form

Note by Raymond Park
1 year, 10 months ago

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:

Thx i learned so much

- 1 year, 9 months ago

These observations are a result of the following fact:

$0.\overline{d_1d_2 \cdots d_n}=\frac{d_1d_2 \cdots d_n}{10^n-1}$ where $$d_1, d_2, \cdots, d_n$$ denote digits.

The proof is quite simple.

- 1 year, 10 months ago