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Math Help: Repeating Decimals

SphinxnihpS

SphinxnihpS

Diamond Member
I need to represent the following numbers as fractions. Show your work.

.5... (point five repeating)

17.9898989898... (98 repeat)

136.25793682091111111111111... (1 repeats)
 
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!
 
jaedaliu said:
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!
Click to expand...

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