Question

Express 1.4191919... In form p/q where p and q are intergers and q not equal 0

Answer 1

Here x = 1.41919......................

So, 10x = 14.1919....................  (i)

and 1000x = 1419.1919..........  (ii)

Subtracting (i) from (ii), we get:

1000x - 10x = 1419.1919........... - 14.1919..................

990x = 1405

x = 1405 / 990 = 281 / 198

So p/q form: 281/198

Answer 2

$let \: x = 1.41919 ......eq.1 \\ now \: sub \: eq1from \: 100 \\ 100x - x = 1.41919 - 141.1919 \\ 99x = 138.78 \\ x = \frac{138.78}{99}$