Question

0. 4 bar________
express the following decimal into rational form.​

Answer 1

Answer:

4/9

Step-by-step explanation:

IN THE PIC

HOPE THIS HELPS

Answer 2

$\sf\purple{Let \:us \:consider \:the\: number (0.4 bar) as (x)}$

So, we get our first equation :

$\sf\pink{x = 0.4444444444444........or 0.4bar}$

The number of digits after the decimal point is called periodicity.

The periodicity in the given number is : 1

So , we will multiply 10 on both the sides to move the decimal to one place to right so that we can do the further operations. We have took specifically 10 as 10 is the only number with a single zero after the digit 1.

Then we get our second equation:

$\sf\pink{10x = 4.4444444.........}$

Now we will Subtract EQUATION 1 from EQUATION 2.

$\longrightarrow{\sf\purple{ 10x-x =4.444....(-)0.44444...}}$

$\longrightarrow{\sf\purple{9x=4}}$

$\implies{\sf\purple{x = \frac{4}{9}}}$