math helps?

Simple.
Follow these steps.
0.01+123/100+123/100000...
a1=123/100
r=1/1000
s inf=a1/(1-r)
Then you add 1/100
=41333/33300
Use the same method but this time, 'make' out the 3.
You get 22/7, about pi.

first you find the repeating sequence
like in 1.24123123123.... it is 123123123
now suppose 1.24123123123...=x
multiply x by that power of ten such that before decimal there is only no repeating sequence like in this case we will multiply by 10 to power 2
now 100x=124.123123...(equation 1)
now multiply x by that power of ten such that before decimal there is only one repeating sequence like in this case we will multiply by 10 to power 5
now 100000x=124123.123123123.....(equation 2)
now if u subtract first equation from this one
u get 99900x=123999
or, x=123999/99900
=41333/33300

but in other problem decimal is already at a place such that there is no repeating unit before decimal
so x=3.142857142857142857
1000000x=3142857.142857142857
subtracting
999999x=3142854
x=3142854/999999

If you can immediately spot that #2 is equal to this, just solve:

3 + (1/7)
= (21/7)+(1/7)
= (22/7)

===========================
#2
Another way is this:

Let x = 3 . 142857 142857

locate the set of repeating decimals then isolate it to the other side by multiplying 10^(number of digits of the repeating decimal) so we can subtract later such that repeating decimals will be gone.

In this case, multiply both sides by 10^6 / 1 000 000

1,000,000x = 3142857 . 142857
x = 3 . 142857

subtract both sides:

999,999x = 3 142 854

x = 3142854 / 999999, which simplifies to 22/7

======================================

do the same for #1 to check your answer:

let x = 1.24123123123

100000x = 124123.123123
100x = 124.123123123
___________________________
99 900x = 123 999

x = 123 999 / 99 900, which simplifies to 41333/33300

Simple it is!
x=1.24123123123...=
100x = 124.123123123....
100x - 124 = 0.123123123..= 123/999
now solve for x
second is now simpler!

1)
x = 1.24123123123123...

1000x = 1241.23123123123...
1000x - x = 1241.23123123123... - 1.24123123123123...
999x = 1239.99
x = 1239.99/999
x = 123999/99900
x = 41333/33300

= = = = = = = =

2)
x = 3.142857142857142857...

1000000x = 3142857.142857142857...
1000000x - x = 3142857.142857142957... - 3.142857142857...
999999x = 3142854
x = 3142854/999999
x = 22/7