Question

write the following rational number in decimal form and say what kind of decimal expansion it has:
1) 0.1888888888....​

Answer 1

x=0.18bar

10x=1.88bar

Thus 9x=1.7

x=1.7/9

x=17/90

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Answer 2

Answer:

0.18888...

is similar to 0.18bar

let x= 0.18bar--1

1*10

10x = 1.8bar---2

now

2*10

100x= 18.8bar---3

3-2

100x-10x=18.8bar- 1.8bar

90x=17

therefore

x=17/90

this is non termenating and recurring