Question

Write the p/q from of 23.(23)bar

Answer 1

Answer:

2320/99

Step-by-step explanation:

let 23.23bar=x.........(1)

multiply both sides by 100

2323.23bar=100x.....(2)

subtract(1)from (2)

100x-x=2323.23bar-23.23bar

99x=2300

x=2300/99

Answer 2

Answer:

2300/99

Step-by-step explanation:

To put the number in the form of p/q, we need to get rid of the recursive digits behind the number.

Define x:

$\text {Let x be } 23.\overline{23}$

Find 100x:

$x = 23.\overline{23}$

$100x = 23.\overline{23} \times 100$

$100x = 2323.\overline{23}$

Subtract x from 100x:

$100x - x = 2323.\overline{23} - 23.\overline{23}$

$99x = 2300$

Find x:

$99x = 2300$

$x = \dfrac{2300}{99}$

Answer: x = 2300/99