Question

Express the following in a $\frac{p}{q} form$
0.003232323232....

Answer 1

Guys, refer to the attachment.

As 32 is repeating continuously , it will be written 32 bar.

Steps to solve the question :

Step 1: Take x = 0.0032 and give it the name equation 1.

Step 2: Multiply 100 on both sides ( because 2 numbers are repeating i. e. 3 and 2) .

Step 3: Find the product and give it the name equation 2.

Step 4: Subtract equation two from equation one .

Step 5: The answer you will get will be in p by Q form .

Answer 2

$x = 0.00323232 \\ \\ 100x = 0.003232 \times 100 \\ \\ 100x = 0.3232 \\ \\ 10000x = 32.323232 \\ \\ 10000x = 32 + 100x \\ \\ 10000x - 100x = 32 \\ \\ 9900 x= 32 \\ \\ x = \frac{32}{9900}$

$\frac{p}{q} = \frac{32}{9900}$

Explanation

Let Given Number as x=0.003232

You will see that 32 is repeating

Firstly Keep 00 at right side of decimal

Zeroes are 2 so Multiply 100 to it

makes 100x=0.3232

32 is Repeating

To make 32 side to Decimal Multiply 100 one time more

100x×100=0.3232×100

10000x=32.3232

Now 0.3232 is 100x

10000x=32+100x

10000x-100x=32

9900x=32

x=32/9900

$\frac{p}{q} = \frac{32}{9900}$