NCERT grade 9 chapter 3 - numbers

1. Prove that if p/q is a rational number in its lowest form then it will terminate if and only if denominator = 2^m.5^n and m,n are whole numbers. And the number of decimals will be max(m,n).
2. Prove sqrt(2) is irrational. (Assume it isn't and then p/q and p,q are both even).
3. a < (a+b)/2 < b for all real a,b
4. Fact: A rational number in decimal form will either terminate or start repeating after some digits. It's not possible for a rational to never terminate and not cycle at the same time.
5. Fact: Pie = 4 * (1/1 - 1/3 + 1/5 - 1/7 + 1/9 ...) Basically alternating odd denominators.


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