Limiting Sum of a G.S Help please (recurring decimals) (1 Viewer)

[Redyapper]

Hi, I need a bit of help doing this question about recurring decimals. The question is:
Express the following recurring decimals as fractions in their lowest terms.
The one I'm having trouble with is 0.43 with the dot above the 3.

For other questions, I knew what to do because all the numbers after the d.p had a dot, e.g.
For 0.25 (dot over both 2 and 5)
I did 25/100 + 25/10000 + 25/1000000 + ...
a= 25/100, r=1/100
S= 25/99

Just confused about what to do now with the 0.43 question.
Thanks in advance!

 

[Peeik]

Not on a computer atm, but think of it as 0.4+(0.03+0.003+...).
Hope i didnt make a mistake.

 

[Shadowdude]

Can't you just use:

Let x = 0.4333...

So 100x = 43.333...
and 10x = 4.333...

So 90x = 39
x = 39/90

 

[Peeik]

^ Some questions specify that use must find it as a limiting sum.

 

[Shadowdude]

Ah okay, then yes - your method is the way to go.


Of course, if the question doesn't specify - take your pick.

 

[jarrodoliver1]

Techinically, you could use any way possible, correct? They don't mark the working out if the answer is correct?

Also, wouldn't it be
n=0.4333
10n = 4.3333
9n = 4
therefore
n=4/9

 

[nightweaver066]

Techinically, you could use any way possible, correct? They don't mark the working out if the answer is correct?

Also, wouldn't it be
n=0.4333
10n = 4.3333
9n = 4
therefore
n=4/9

No.

 

[Shadowdude]

Techinically, you could use any way possible, correct? They don't mark the working out if the answer is correct?

Also, wouldn't it be
n=0.4333
10n = 4.3333
9n = 4
therefore
n=4/9

If it says to set it up as a limiting sum, you'd get it wrong. Maybe 1 mark out of say... 3 for getting the right answer - but the other two comes from setting r and a and all that other geometric limiting sum whatnot.