Math Help: Repeating Decimals

SphinxnihpS

Diamond Member
Feb 17, 2005
8,368
25
91
I need to represent the following numbers as fractions. Show your work.

.5... (point five repeating)

17.9898989898... (98 repeat)

136.25793682091111111111111... (1 repeats)
 

jaedaliu

Platinum Member
Feb 25, 2005
2,670
1
81
divide by 9 for repeats, 0 for non-repeats.

.5555... is 5/9

.696969.... is 69/99 (not that is not simplest terms)

then I can't remember the other stuff.
.12333333 is something like (123-12)/900 or something like that.

good luck with google!
 

Dari

Lifer
Oct 25, 2002
17,133
38
91
My HP 48G is able to turn decimals into fractions. Download an emulator.
 

SphinxnihpS

Diamond Member
Feb 17, 2005
8,368
25
91
divide by 9 for repeats, 0 for non-repeats.

.5555... is 5/9

.696969.... is 69/99 (not that is not simplest terms)

then I can't remember the other stuff.
.12333333 is something like (123-12)/900 or something like that.

good luck with google!

I don't want cheap parlor tricks, I want Xs. This is my google.
 

Dari

Lifer
Oct 25, 2002
17,133
38
91
Glad someone was able to help you out. I remember in undergrad, a lot of the math PhD candidates, when helping students out, would forget how to do simple math like add and subtract. I guess the old adage of "use it or lose it" is true. When you're doing really advanced work you sometimes have to remember how to do the most basic things...
 

Binarycow

Golden Member
Jan 10, 2010
1,238
2
76
Use a geometric series and you can do it the proper way for all repeated decimals.
 

DrPizza

Administrator Elite Member Goat Whisperer
Mar 5, 2001
49,601
166
111
www.slatebrookfarm.com
17.98989898... (show your work)

10
---- x 17.98989898...
10

179.89898989898...
--------------------------
10

Ta da!

(You didn't say it had to be a proper fraction.)
 

dighn

Lifer
Aug 12, 2001
22,820
4
81
0.121212... = 12 * (1/100^1 + 1/100^2 + ...)
= 12 * (1/(1 - 1/100) - 1) => geometric series
= 12 * (100 / 99 - 1)
= 12 / 99

btw this is only a trick because 0.999... != 1
 
Last edited:

phucheneh

Diamond Member
Jun 30, 2012
7,306
5
0
It's 1. If the 9 repeats infinitely, there will never be a '...01' to subtract from it.

Advanced math doesn't work on common sense, though, so some jackass probably wrote a proof for the '.99... != 1' concept.
 

SagaLore

Elite Member
Dec 18, 2001
24,036
21
81
It's 1. If the 9 repeats infinitely, there will never be a '...01' to subtract from it.

Advanced math doesn't work on common sense, though, so some jackass probably wrote a proof for the '.99... != 1' concept.


:sneaky:
 

Aikouka

Lifer
Nov 27, 2001
30,383
912
126
I found that method of figuring out the fraction rather interesting, because I don't think I've ever seen that before! What grade level were you supposed to learn that sort of thing at?