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