Question

the p/q form of 0.366666 is​

Answer 1

Answer:

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Answer 2

Answer:

The  $\frac{p}{q}$ form of 0.36666.....= $\frac{11}{30}$

Step-by-step explanation:

Given recurring decimal number is 0.3666.......

To find the $\frac{p}{q}$ form of the given recurring decimal number

Recall the concept

Every recurring decimal numbers are rational numbers and hence every recurring decimal number can be written in the form  $\frac{p}{q}$ , where 'p' and 'q' are integers and q ≠0

Solution:

Let x = 0.36666...... --------------------(1)

Since, there is one decimal place that is not recurring, multiplying the equation (1) by 10 we get

10x = 0.36666......×10

10x = 3.6666.......... --------------------(2)

Since, there is one recurring decimal place, multiplying the equation (2) by 10 we get

100x =  3.6666..........×10

100x = 36.666............. -----------------(3)

Subtracting (2) from equation (3)

(3) -(2) →

100x - 10x = 36.666............ - 3.6666..........

90x = 33

x = $\frac{33}{90}$ = $\frac{11}{30}$

0.36666......= $\frac{11}{30}$

The  $\frac{p}{q}$ form of 0.36666......= $\frac{11}{30}$

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