Question

write 0.1311111.... in o/q form​

Answer 1

Explanation:

Given :-

0.1311111...

To find :-

Write p/q form of the given decimal number ?

Solution :-

Given decimal number = 0.131111...

Let X = 0.131111...------------(1)

Since the periodicity is 1 ,we multiply equation (1) with 10 then

X× 10 = 0.131111...× 10

10X = 1.31111...---------------(2)

On Subtracting equation (1) from equation (2)

(2) - (1) =>

10X = 1.31111 ...

X =0.13111...

(-)

___________

9X = 1.18000...

____________

=> 9X = 1.18

=> 9X = 118/100

=> X = (118/100)/9

=>X = 118/(100×9)

=> X = 118/900

=>X = 59/450

Therefore, 0.131111... = 59/450

Answer:-

The p/q form of the given decimal number 0.13111... is 59/450

Used formulae:-

Periodicity:-

The number of digits in the recurring part of the decimal number is called its periodicity.

Additional information:-

• Every rational number can be written as either a terminating decimal or a non terminating and non recurring decimal.

• The number of digits in the recurring part is periodicity and the group of digits in the recurring part is called the period.

Ex :-2.6666..= 2.6bar

• Period = 6

• Periodicity = 1

Answer 2

Answer:

1311111/10000000

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