Express decimal form of a number in rational form | Convert decimal expansion in rational number

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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.

00:05 rational form p/q of decimal form 0.6666....

00:14 (ii) Convert decimal form of a number 0.477777 in rational form p/q .

02:33 rational number of decimal expansion 0.477777 is 43/90.

02:55 (iii) Write decimal form of a number 0.001001001001.... in rational form p/q

03:25 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.

04:51 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.

05:48 Multiplying both sides of equation by 10.

Here, one digit 9 is repeating

06:10 Subtract one equation from other

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

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