Question

Express 0.26(bar on 6)+0.31(bar on 1) in the form / where and are integers and ≠0.

Answer 1

Answer:

0.2666666....... =  4/ 15 and 0.311111....... = 14/ 45

Step-by-step explanation:

a) 0.266666.....

let x be 0.266666..... --- 1

multiply 1 by 10

10x = 2.66666666......---2

multiply 2 by 10

100x = 26.666....... ---3

subtract 2 from 3

(100 - 10)x = (26.666... - 2.666...)

90x = 24

x = 24 / 90

x = 4 / 15

b)0.3111111.....

let x be 0.311111..... --- 1

multiply 1 by 10

10x = 3.111111111......---2

multiply 2 by 10

100x = 31.111111....... ---3

subtract 2 from 3

(100 - 10)x = (31.1111... - 31.1111...)

90x = 28

x = 28 /90

x = 14 / 45

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