How do you turn a decimal to a fraction

Say you have a number like

12.34

That is, 12 and 34 hundredths. 0.34 is the same as 34/100, so

12.34 = 12 + 34/100 = 1200/100 + 34/100 = 1234/100 = 617/50

If you have a number with repeating digits in the decimal, like

12.343434 ... (with 34 repeating forever)

we can let x be this number. Then

100x = 1234.343434 ...

If we subtract x from 100x, we can eliminate the repeating decimal part:

100x - x = 1234.343434 ... - 12.343434 ...

99x = 1234 - 12

99x = 1222

Then solving for x gives the decimal as a fraction:

x = 1222/99