Converting recurring decimal to fraction?

Question

One question that is bugging me (and have been, ever since that maths test 2 days ago) is this:

"Convert the recurring decimal 0.432 (only the 3 and 2 being recurring numbers with dots on top) into a fraction."

I know how to do the basic thing, and I know how to do it with only recurring decimals, but I just got stuck on the part where there is the "4" which isn't recurring!!

So please explain how I am meant to solve this question??
Yes I know, Im still thinking about a maths question 2 days after a test! It's bugging me!!

Thank you

Answer 1

"Convert the recurring decimal 0.432 (only the 3 and 2 being recurring numbers with dots on top) into a fraction."

Let us try it this way.

x = 0.43232323232 ....

Multiply by 10, so that only recurring part is on the right of decimal.

10x = 4.3232323232 .... (1)

As there are 2 recurring numbers, multiply equation (1) by 10^2 = 100

100*10x = 432.32323232 .... (2)

In equations (1) and (2), value of .32 ... is same as 32 is recurring number.

Subtract equation (1) from (2),

1000x - 10x = 432.32323232 .... - 4.3232323232 .... = 428

or 990x = 428

Therefore x = 428 / 990 = 214 / 495

Using Excel, 214 / 495 = 0.432323232323232 QED

Does it make sense?

Answer 2

1 non-repeating digit after the decimal = one 0. 2 repeating digits after the decimal = 2 9's. Subtract the non-repeating part from the rest: 136 - 1 = 135 So the fraction is 135 / 990 (990 from the 2 9's and 1 0.) Simplify to get = 27 / 198 = 3 / 22 and add the 2 to get 2 3/22

Answer 3

0.432 (with dots on 32) means 0.4323232323232.......

Now write the recurring decimal fraction as

0.4323232323232.......

=0.4+.03232323232.....and proceed now