Write non - terminating repeating decimal expansion in rational form p/q where q is not zero

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In the above discussion, we have seen that a rational number of the form has either a

terminating decimal expansion or a non - terminating repeating decimal expansion and

conversely that a terminating or a non - terminating and repeating decimal expansion can

be converted into the form p/q , where p and q are integers , and q is not zero 0 .

A terminating or a non - terminating and repeating decimal expansion can be converted into the form p/q, where p and q are integers , and q is not 0 .

00:02 Q3. Express the following in the form p/q, where p and q are integers and q is not 0.

00:18 (i) Express decimal form of a number 0.6666.. in rational form p/q.

00:39 Multiplying both sides of equation by 10.

Here, one digit 6 is repeating

02:05 rational form p/q of decimal form 0.6666....

02:15 (ii) Convert decimal form of a number 0.477777 in rational form p/q .

04:34 rational number of decimal expansion 0.477777 is 43/90.

(iii) Write decimal form of a number 0.001001001001.... in rational form p/q

05:26 Multiplying both sides of equation by 1000.

Here, three digits 001 is repeating.

A number whose decimal expansion is terminating or non-terminating recurring is rational.

06:52 Q4. Express decimal expansion 0.99999 .... in the rational form p/q. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

07:49 Multiplying both sides of equation by 10.

Here, one digit 9 is repeating

08:11 Subtract one equation from other

08:04 rational form p/q of decimal expansion 0.99999 .... is 1

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