Limiting Sum recurring decimal (1 Viewer)

[atakach99]

Write 0.25252525 as a fraction

i know how to do it the other way that i learnt in yr 11 but dont know how to find it using limiting sum formula..
plz help
thnks

 

[lyounamu]

Write 0.25252525 as a fraction

i know how to do it the other way that i learnt in yr 11 but dont know how to find it using limiting sum formula..
plz help
thnks

divide 0.25252525.... into 0.25 + 0.0025 + 0.000025 +.....
and then use limiting sum formula

from here u can see that a = 0.25 and r = 0.01

so use the formula and you will find it.

 

[atakach99]

thnks man....good to see that i am not the only one studying on a sunday .. lol

 

[lyounamu]

thnks man....good to see that i am not the only one studying on a sunday .. lol

Lol.. I am not studying...... but I think I should now.

 

[atakach99]

wll what about this one...

2.888888888

how can i write that in a fraction using the formula of limiting sum

 

[lyounamu]

wll what about this one...

2.888888888

how can i write that in a fraction using the formula of limiting sum

separate 2.888888... like 2 + 0.88888... and then
2 + 0.888888... = 2+ 0.8 + 0.08 + 0.008 +.....
= 2 + and the limiting sum formula where a = 0.8 and r = 0.1

when you get the question like that, always separate the series from the number. So that you can apply your formula for the question

Cheers

 

[atakach99]

thnks mate

 

[lyounamu]

thnks mate

no problemo... doing few questions of that will help you getting through that more easily.

 

[Slidey]

So!

Can somebody tell me what

0.16... + 0.16... + 0.16... + 0.16... + 0.16... + 0.16... equals?

... means repeater in this case (the 6 not the 1).

 

[foram]

So!

Can somebody tell me what

0.16... + 0.16... + 0.16... + 0.16... + 0.16... + 0.16... equals?

... means repeater in this case (the 6 not the 1).

let x=0.16...
10x = 1.6...
100x = 16.6...
90x = 16
x=16/90

6x = 16(6)/90
6x = 16/15

 

[vds700]

let x=0.16...
10x = 1.6...
100x = 16.6...
90x = 16
x=16/90

6x = 16(6)/90
6x = 16/15

isn't 90x = 15
so x = 15/90

check by calc, 15/90 = 0.166666....

 

[lyounamu]

isn't 90x = 15
so x = 15/90

check by calc, 15/90 = 0.166666....

That seems right... hi Andrew! helping some people out there?

 

[foram]

let x=0.16...
10x = 1.6...
100x = 16.6...
90x = 15
x=15/90

6x = 15(6)/90
6x = 1


Careless of me .

 

[Slidey]

Hehe. I was basically asking what 6*1/6 was.

Some people get caught up by the idea that 0.333... + 0.333... + 0.333... equals one. They might say "but no, it equals 0.999..." and it does, but because it's a geometric series limit, it also equals 1.

0.999... = 9/10 + 9/100 + 9/1000 + ...
= 9(10^-1 + 10^-2 + 10^-3 + ...)
= Lim to infinity of Sum 9*10^-n from one to n.
= Lim to inf (9/10)*(1-10^-n)/(9/10)
= Lim to inf (1-1^-n)
= 1

Interestingly, you can also use this method for any repeating decimal, instead of the 10x method, because the denary (decimal) number system is made up of powers of 10 up to infinity.

E.g.: what is the value of 12.34(5...)? That is the 5 only repeats.
12.345... = 12.3455...
So 12.34 + (0.005 + 0.0005 + ...)
= 12.34 + 5*(10^-3 + 10^-4 + ...)
= 1234/100 + Lim to inf of Sum (5*10^-n-3)
= 1234/100 + Lim to inf of Sum (5/1000*10^-n)
= 1234/100 + 5/1000 * 1/(1-1/10) (sum to infinity of any converging geometric series equals a/(1-r))
= 1234/100 + 5/900 (now just find a common denominator)
= 11111/900 woo

And:
0.11... = 10^-1 + ...
So it equals 1/10/(1-1/10) = (1/10) / (9/10) = 1/9