Find two rational numbers of the form p/q between 0. 212212221... and 0.2020020002...
harshitsingh798:
devikas someone deleted my answers were they wrong?
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2,020,020,003/10,000,000,000
Or, .2020020003.
I choose this ridiculous number to show that any decimal that does not infinitely repeat is a rational number because we can simply divide it by a power of 10.
So all we have to do is pick a finite, ending number between the two and then pick the denominator.
How about 0.21, to keep it simpler than before.
21/100
Or, if you dont want a power of 10 on the bottom, pick one that shares a factor with 10.
205/1000 = 41/200
Or, .2020020003.
I choose this ridiculous number to show that any decimal that does not infinitely repeat is a rational number because we can simply divide it by a power of 10.
So all we have to do is pick a finite, ending number between the two and then pick the denominator.
How about 0.21, to keep it simpler than before.
21/100
Or, if you dont want a power of 10 on the bottom, pick one that shares a factor with 10.
205/1000 = 41/200
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