Recurring Decimals
You can expect two types of questions here:
1) Convert 0.33333... into a fraction
2) Convert 1/3 into a recurring decimal
Number 2 is generally easier to do.
How to do Number 1
First you need to define a variable to be the recurring decimal.
x = 0.3333...
Let this equation be ....A
Now that you can see that x has been defined, we will multiply both sides by such a number(a multiple of 10) that will let the new equation when it is subtracted with equation A, it will return a whole number value.
Didn't understand??
In simpler words...
x = 0.5555
10 x = 5.5555
So when we subtract second from first,
we get 9x = 5 <----- look we got a whole number
x = 0.456456456...
10 x = 4.565656...
Now here, subtracting the first from second wont return a whole number value so we need to add another equation.
x = 0.456456456.. --A
10x = 4.56456456.. ---B
100 x = 45.6456456.. ---C
1000x = 456.456456456.. --D
As you can see when we subtract B or C from A, we dont get a whole number value.
However, D - A will give a whole number value and this will answer the question.
x 0.456456456... -A
1000x = 456.456456456... -D
A-D
999x = 456
x = 456/999
Simplify
x = 152/333
This is a harder question ^^ for IGCSE level but ofcourse there are harder ones we will look at later.
Lets get back to the question we started with
x = 0.33333.. -1
10x = 3.3333.. -2
Doing 2-1
9x = 3
x = 1/3
Harder Questions---
