Question

Express 1.143bar in the form p/q where p and are integers

Answer 1

Answer:

1132/990

Step-by-step explanation:

To Express :-

$1.1\overline{43}$ in the form of p/q.

How To Do :-

As they given a equation first of all we need to remove the bar from the equation and we need to convert it also in the decimal form. And we need to simplify it to get the required value.

Solution :-

$1.1\overline{43}$

= 1 . 1 43 43 43 43 ...

Let,

x = 1.1 43 43 43 43 ..

[Let it be equation - 1]

Multiplying equation - 1 with 100 :-

100 × x = 100 × (1 . 1 43 43 43 43 ..)

100x = 114. 3 43 43 43 43 ...

[ Let, it be equation - 2]

Subtracting equation 1 from equation 2 :-

100x - x = (114. 3 43 43 43 43 ..) - (1. 1 43 43 43 43...)

99x = 114. 3 43 43 43 43 ... - 1 . 1 43 43 43 43 ..

99x = 113. 2

x = 113.2/99

Multiplying and dividing with 10 in R.H.S :-

x = 113.2/99 × 10/10

x = 1132/990

∴ $1.1\overline{43}$ = 1132/990.