Question

express 0.43 (bar on 3) in the p/q form?

Answer 1

Here is your answer it may help...

Answer 2

Answer:

 $\frac{39}{90}$

Step-by-step explanation:

Given:- The given decimal number is 0.4333......

To Find:- Express the above decimal number in the p/q form.

Solution:-

The given number 0.43333... is a Recurring or Repeating decimal.

Here we need the express the given number in the form of a fraction p/q.

Let x = 0.43333....      ----- ( 1 )

There is only one digit before the repeating of the digit starts.

Multiplying both the sides by 10 in equation ( 1 ), we get

∴ 10x = 4.333....      ----- ( 2 )

Now the multiplying both the sides of equation ( 2 ) by 10, we get

100x = 43.3333....   -------- ( 3 )

Now, substracting equation ( 2 ) from ( 3 ) i.e. ( 3 ) - ( 2 ), we get

⇒ 100x - 10x = 43.33... - 4.333...

⇒ 90x = 39

⇒ x = 39 ÷ 90

⇒ x = $\frac{39}{90}$

Therefore, p/q form of 0.43333.... is  $\frac{39}{90}$.

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