SOLUTION: write irrational number between 0.3010010001....and 0.3030030003....

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Question 1081729: write irrational number between 0.3010010001....and 0.3030030003....
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
.3010010001... < +highlight%28sqrt%2891205%2F1000000%29%29+ < 0.3030030003…
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Found this as follows:
1. Clearly 0.302 is in the range required.
2. 1000*0.302 = 302
3. 302^2 = 91204
4. 91204 + 1 = 91205 (and sqrt(91205) is guaranteed to be irrational since it is perfect square + 1 and the distance to the next perfect square (303^2) is much greater than 1).
5. Just add the denominator of 1000000 to line up the decimal place.