Question

"Question 4 Express 0.99999…in the form p/q. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense. Class 9 - Math - Number Systems Page 14"

Answer 1

Given:
0.9 = 0.99999…
Let x = 0.99999……. (1)

Here only one digit is repeating so multiply by 10 on both sides

10 × x = 10× 0.99999….
10x = 9.9999…. (2)
On subtracting equation 1 from equation 2

10x- x = 9.9999…. - 0.9999….

9x = 9

x = 9/ 9 = 1

Here , 0.9 = 1

Yes we are surprised to get an integer 1, because 0.9999…. goes on forever so there is no gap between 1 and 0.999 9... and hence they are equal.

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Hope this will help you ...

Answer 2

Answer: express 0.999--in form of p/q

X=0.99999----(I) equation

Next equation multiply by 10 both the side,so we get

10x=9.99999----(ii)

Subtracting (ii) equation from(I) equation,we get

10x=9.99999----

- x=0.99999----

__________________

9x=9

___________________

X=9/9

X=1/1

Answere=0.9999---- =1/1 in the form of p/q.

Step-by-step explanation:Yrr remark

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