
PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoThe decimal expansion of a rational number is terminating or non-terminating and recurring. Conversely, the decimal expansion of a number is terminating, or non-terminating recurring is a rational number.
Example:
1. Prove that 0.77777... = 0. is a rational number. That is, show that 0. can be expressed in p/q, where 'p' and 'q' are integers with q0.
Solution:
Let us take the provided number as 'x'.
That is x\ =\ 0.77777...
Now observe the number 'x'. The only repeated digit is 7.
Here we have to make multiples of 'x' in such a way that its decimal part will be the same as the given number.
Let us multiply 'x' by 10.
10x\ =\ 7.77777...
Now subtract 'x' from 10x,
10x - x = 7.77777... - 0.777777...
9x = 7
x = 7/9
Therefore, the fractional form of the rational number 0. is 7/9.
2. Prove that 0 .2363636...\ =\ 0.2 is a rational number. That is, show that 0.2 can be expressed in p/q, where 'p' and 'q' are integers with q0.
Solution:
Let us take the provided number as 'x'.
That is x = 0.2363636...
Now observe the number 'x'. There are two repeated digits. That is 36.
Here we have to make multiples of 'x' in such a way that its decimal part will be the same as the given number.
Also, we have one non-repeating number 2.
10x\ =\ 2.363636...
Now multiply 'x' by 1000 to get the same decimal pars of 10x,
1000x\ =\ 236.363636...
Subtract 10x from 1000x.
1000x - 10x = 236.363636... - 2.363636...
990x\ =\ 234
x\ =\ 234/990
Therefore, the fractional form of the rational number 0.2 is 234/990.