Asked by Lalalay

How you would convert the repeating, nonterminating decimal to a fraction? Explain the process as you solve the problem. 0. 1515..
Answered by Bosnian
x = 0.1515...

100 x = 15.1515...

100 x - x = 15.1515... - 0.1515...

99 x = 15

x = 15 / 99 = 3 ∙ 5 / 3 ∙ 33 = 5 / 33


0.1515... = 5 / 33
Answered by Reiny
algebraic method:
let x = .151515....
multiply by 100 , (since the repeat cycle is 2 digits so need 10^2 as a multiplier)
100x = 15.151515...
subtract them
99x = 15.0000...
x = 15/99 = 5/33

always check your result with a calculator, this one works


get's a little trickier if some of the digits don't repeat,
e.g. 0.23456456456...
let x = 0.23456456456...
I multiply both sides by 1000, (see reason above)
1000 = 234.56456456...
subtract them:
999x = 234.3300000... = 234.33
but we don't want a decimal in our answer, so

99900x = 23433
x = 23433/99900= 7811/33300 , check with calculator

quick way: using my last example
for the numerator :
write down the sequence of digits to the end of the first repeat
23456
subtract the sequence of digits that DON'T repeat
23456 - 23 = 23433

for the denominator:
write down a 9 for each repeating digit. There are 3 digits repeating, so
999
followed by a 0 for each of the non-repeating digits, so
99900
your fraction is 23433/99900
reduce it to my previous answer

works for simple cases:
e.g. 0.222222....
numerator: 2-0 = 2
denominator = 9 , one digit repeated, so one 9, followed by no zeros
.22222... = 2/9
Answered by oobleck
or, let x = 0.23456456456...
multiply by 100 to get
100x = 23.<u>456</u> = 23 456/999
x = 23/1000 + 456/99900 = (23*999+456)/99900 = 23433/99900
as above
Answered by Lalalay
Thank you
Answered by Katherine
x = 0.1515...

100 x = 15.1515...

100 x - x = 15.1515... - 0.1515...

99 x = 15

x = 15 / 99 = 3 ∙ 5 / 3 ∙ 33 = 5 / 33

0.1515... = 5 / 33


Answered by That Crusader
Lord have mercy
Answered by Aren
Helpful 😀
Answered by ummm....
I
Am
So
Dead

...

Lord save me before I start punching a tree.

I am seriously so confused as to how any of this works. I know that You have to convert the original number (being 0.1515...) to "x" but I don't understand the series of things to help convert the number to a fraction. it almost looks like random numbers you chose (Katherine) to show that this is a number that can be multiplied by, or something along those lines. I'm gonna keep trying to figure this out, thanks guys!
Answered by koolkid
thx @bosian, I got 100% with your answer. Thx soo much!!
Answered by him
I'm with ummm.... I don't understand
Answered by him
can koolkid explain since their from today
Answered by i have a $100 target gift card
is the / in it for fractions or division
Answered by ineedtheanswer
boasian or whatever is right
Answered by uh
I don't understand
Answered by wow
high school dxd
Answered by (╯°□°）╯︵ ┻━┻
bruh who is correct
Answered by 010
I dont get it
Answered by Hey! [she/they]
My brain is going to explode oh god today is the day i die. Lord have mercy and forgive me of all me sins. I am going to cry, so many numbers and letters are going on my brain is too small to take it all in. All i wanted was an example that i understand to take inspiration from, holy shart may the lord have mercy on my soul
r.i.p
Answered by John Doe
Could some explain a bit more in depth how to solve the problem, it's just a little difficult for me. I don't want the answer, I just want to know how to solve this problem.
Answered by Anonymous
..welp
Answered by misa
imma cry fr
Answered by guy
bruh 💀
Answered by dude
seeing you guys struggle is a struggle for me because im also struggling💀
Answered by top gun bob
bro this is pain
Answered by im
gonna cry
Answered by Zero
atp im going to wwork at mcdonalds bro
Answered by Joe mama
@Zero Fr bro, I can't do this crap anymore. I'm going to go insane.😭😭
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