Answer the question in the image

Question

asked Mar 28, 2023 158k views

2 Answers

Zheng Qsin · Answer 1 · 2023-03-29T15:02:41+0000

Answer:

(211)/(500)

Explanation:

$.4\bar{2}$ means the 2 repeats till infinity

$.4\bar{2}$ = .4222222222.....

To convert to fraction just take the first three decimal place digits 422 and divide by 1000 to convert to fraction

$.4\bar{2} = (422)/(1000)$

Dividing numerator and denominator of this fraction by 2 gives

(422/2)/(1000/2) =(211)/(500)

This cannot be simplified further and therefore

$.4\bar{2} = (211)/(500)$

If we had chosen first 4 decimal digits then it would be
$.4\bar{2} = (4222)/(10000) = (2111)/(5000)$
i.e. we divide by 10,000