Question

convert in the form of p/q 0.111...​

Answer 1

Answer:

Step by step process shown below:

Step-by-step explanation:

First take x = 0.111... (1st equation)

Then next multiply 10 on both the sides as there is only one number recurring after the decimal.That is

10*x = 10*0.111...    (2nd equation)

Next, subtract the first equation from the second equation :

10x - x = 1.11... - 0.111

= 9x = 1

=x = 1/9

That is it.....

Answer 2

GIVEN :-

• $\text{ that we have number 0.111}$

TO FIND :-

• $\text{ we have value of 0.111 in p/q form }$

SOLUTION :-

$\text{ let value \: of \: x= 0.111 ---eq1}$

$\implies \text{ \: value \: of \: 10x \: = 1.111 ---eq2}$

NOW SUBTRACT EQ1 FROM EQ 2

$\implies \text{ 10 x - x \: = \: 1.111 \ - 0.111 }$

$\implies \text{ 9x \: = 1}$

$\implies \boxed{ \boxed{ \mathrm{ x = \frac{1}{9} }}}$

OTHER INFORMATION:-

To convert a decimal number into p/q form, follow the following steps.

• Check whether the decimal number is non terminating non recurring decimal or non terminating recurring decimal or terminating decimal.

• if it is non terminating non recurring decimal number, you cannot convert it into p/q form, since it is an irrational number.

• If it is a terminating decimal, follow the procedure given below.

• Find the number of decimal places in the given decimal number.

• Take 1 annexed with as many zeroes as the number of decimal places given in the decimal.

• Multiply and divide the given decimal with this number.

• If the given decimal is non terminating recurring decimal, follow the procedure