Question

express 1.4191919.......... in the form of p/q where p and q are integers and q is not equal to zero

Answer 1

Answer:

The right answer p/q form: 281/198

Step-by-step explanation:

In given situation…….  

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

We get the equations………….  

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

Answer:

p = 281 and q = 198

Step-by-step explanation:

Since we want to express 1.4191919.......... in the form of p/q where p and q are integers and q is not equal to zero:

Let x = 1.4(19)

Then, if we multiply both sides by ten, we get:

⇒ 10x = 14.(19)

and also, instead of ten, we multiply by one thousand and we conclude the following:

⇒ 1000x = 1419.(19)

Now if we subtract the first expression from the second one, we will reach the result we are looking for, thus, we have that:

⇒ 1000x - 10x = 1419.(19) - 14.(19)

⇔ 990x = 1405

⇒ x = 1405 / 990 = 281 / 198

Therefore our integer number in form p/q are p = 281 and q = 198.