In Example 3, change the decimal form to 0.012012012 . . . .

Data from Example 3

Find the fraction that has its decimal form 0.121212 . . . . This decimal form can be considered as being 0.12 + 0.0012 + 0.000012 + . . . which means that we have an infinite geometric series in which a 0.12 1 = and r = 0.01. Thus,

Therefore, the decimal 0.121212 . . . and the fraction 4/33 represent the same number.

S || 0.12 1 - 0.01 4 33 0.12 0.99