Question

pls in detail
I so argent for me pls be fast​

Answer 1

Answer:

4/9

Step-by-step explanation:

To find :

• p/q form of $\sf{0.\overline{4}}$ = ?

Solution :

We know that the given no. is a terminating rational no. We can easily find the p/q form of a non-terminating rational no.

Here, we are given with a terminating rational no. i.e, $\sf{0.\overline{4}}$

If we would given with a non-terminating rational no. such as 0.4, we can easily make it in p/q form by removing the decimal. It will be 4/10 = 2/5. Hence, 2/5 is the p/q form for 0.4.

We have another method for making p/q form for terminating rational no.

First we will have to equate 0.4 or given no. with any variable let us take 'x'.

⇒ x = 0.4 ...(1)

To remove the bar above 4, we have to multiply 10 to both LHS and RHS.

⇒ 10x = 10 × $\sf{0.\overline{4}}$

⇒ 10x = $\sf{4.\overline{4}\:\:\:\:\:...(2)}$

Now, subtract (2) from (1).

We get,

⇒ 10x - x = $\sf{4.\overline{4}\:-\:0.\overline{4}}$

⇒ 9x = 4

⇒ x = 4/9

Therefore, p/q form is 4/9.

_____________________________________

For better understanding, let's try another ques like this !

>> Let's suppose that we have to find the p/q form of $\sf{0.5\overline{27}}$

For this, first we will take 5 out of the decimal places by multiplying it by 10.

⇒ x = $\sf{0.5\overline{27}}$

(Multiply 10 both the sides)

⇒ 10x = $\sf{5.\overline{27}\:\:\:\:\:(1)}$

We have taken 5 out, now we will take out 27 by multiplying 100 both the sides.

⇒ 100 × 10x = $\sf{100\:\times\:5.\overline{27}}$

⇒ 1000 x = $\sf{527.\overline{27}\:\:\:\:\:\:...(2)}$

Now, as our previous ques subtract (2) from (1).

⇒ 1000x - 10x = $\sf{527.\overline{27}\:-\:5.\overline{27}}$

⇒ 990x = 522

⇒ x = 522/990

(If possible simply it futher)

⇒ x = 261/495

Therefore, the p/q form is 261/495.

And we are done ! :D