Question

Use a series to express the following number as a ratio of integers: 0.73737373

Answer 1

\[\frac{73}{100}+\frac{73}{10000}+\frac{73}{1000000}+...\]

Answer 2

Can also be 73/99 If you're doing infinite geometric series

Answer 3

you get
\[\frac{73}{100}\sum_{k=0}^{\infty}(\frac{1}{100})^k\]

Answer 4

and as jlastino wrote, if you add this up you get \(\frac{73}{99}\)

Answer 5

Thank you guys! Can I write 0.2222 as:
\[\sum_{1}^{\infty} 2 (1/10)^{n} = 2/10 \div 1-1/10\] ?? Oh and how are you guys making your fractions look like that?

Answer 6

There's a shortcut for writing repeating decimals haha
You take the repeating part
then divide it by a # of 9's (The number depends on how many numbers repeat)

Which in this case 2

So It can be written as

2/9

Answer 7

Oooooo. My teacher may have said that. But I missed this lesson in class, so Im teaching myself. Thanks again. I SHALL post more!

Answer 8

fractions you write via \frac{a}{b}

Answer 9

and no agony for repeating decimals.
\[\overline{.1}=\frac{1}{9}\]
\[\overline{.2}=\frac{2}{9}\]
\[\overline{.3}=\frac{3}{9}\]
\[\overline{.4}=\frac{4}{9}\]
\[\overline{.5}=\frac{5}{9}\]
etc

Answer 10

Lol, this is great!

Answer 11

More examples:

0.123123123 = 123/999
0.14331433= 1433/9999
0.515151 = 51/99

Answer 12

What about 6.254, with "54" repeating? I have: \[62\sum_{n=1}^{\infty} 54 (\frac{1}{1000})^n\]

Now i just gotta figure out how to solve.

Answer 13

I forgot how to solve (sadly) I just do the shortcut T_T
It'll be
62/10 + 54/990

Ask satelite for help on the solution

Answer 14

I have the same answer: 62/10 + 54/999= 6.2540