Question

Express the following in the form of p/q , where p and q are integers and p/q 0.0032 bar on 3​

Answer 1

Answer:

8/2475

Step-by-step explanation:

Correct Question :-

Express the following in the form of p/q , where p and q are integers and p/q 0.0032 bar on 32.

Given ,

$0.00\overline{32}$

To Find :-

Write in p/q form

How To Do :-

First of all we need to remove the bar and we need to write in normal decimal form , After writing it we need to consider it an equation 1 and we need to multiply in by 100(whole equation) so that there will be no change in the value and we need to consider it as equation - 2 and we need subtract the equation - 1 from equation -2 to obtain the value in the p/q form.

Solution :-

$0.00\overline{32}$

= 0.00 32 32 32 32 ...

Let ,

x = 0. 00 32 32 32 32 ...

[ Let , it be equation - 1]

Multiply '100' with equation - 1 :-

100 × x = 100(0. 00 32 32 32 32 ...)

100x = 0. 32 32 32 32 ...

[ Let it be equation - 2]

Equation 2 - Equation 1 :-

100x - x = 0. 32 32 32 32 ... - 0. 00 32 32 32  ...

99x = 0.32

x = 0.32/99

Multiplying and dividing with 100 :-

x = 0.32/99 × 100/100

x = 32/9900

x = 8/2475 [∴ In simplest form]