Question

Show that 0.3333... =0.3 bar can be expressed in the form p/q, where p and q are integers and q not = 0

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Answer 1

Answer: Let x = 0.333........

So, 10x = 10*0.3333.......

10x = 3.3333.....

10x - x = 3.33..... - 0.33.....

9x = 3

x = 3/9 = 1/3

Therefore, x = 1/3

1/3 is a rational number which is in the form of p/q where p and q are integers and q is not equal to zero.

Hence, 1/3is the correct answer.

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Answer 2

Answer:

Given: 0.3 bar.

So, let us assume variable (a) as 0.3 bar.

⇢a = 0.3333...

⇢10a = 10 × (0.333...) = 3.333...

⇢3.333... = 3 + a

⇢a = 0.333...

⇢10a = 3 + a

⇢9a = 3

⇢a = 1/3