Question

show that 0.73 recurring= 11/15

Answer 1

Answer in attachment

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Answer 2

Given:

0.733333...

To Find:

Find it in the form of p/q

Solution:

To express in the form of p/q we will let the given number be equal to x. Please note that it can be expressed in p/q form only if the decimal is repeating non terminating decimals. now let x=0.733333...

$x=0.733333...$      -(1)

Now multiply it by 10 we have

$10x=7.333333$           -(2)

Now multiply both sides by 10( we choose it to multiply by 10 100 1000 etc depending on the digits after which they are repeating if they are repeating after 4 digits then multiply by 10000)

$100x=73.33333...$     -(3)

Now subtracting equation 3 with equation 2 we get

$90x=66\\\\x=\frac{66}{90}\\=\frac{11}{15}$

Hence, 0.733333 in a fraction is 11/15.