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