Some of the most interesting estimation questions on number sense tests involve the irrational (but real) number Pi (better known as π), which is approximately 3.14159265358979323846264338327950288419716939937510... This concept appeared 9 times last year, with a median placement at question # 70.
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Number Dojo Level: 220
When I was younger, I found it entertaining to try to memorize dozens of digits of π. I don't think I ever got very far, and now, if somebody catches me off guard, I can only recite the first 20 decimal places. (I think my daughter can rattle off about twice that many). One of the many cool things about π is that when you square it, you get about 10. (You actually get about 9.8696044, but for number sense estimation questions, that's close enough!).
How close is close enough?
As you well know, as long as your answer is within (+/-) 5% of the exact answer for estimation questions, it is considered correct. For every two factors of π in a question, you can be safe substituting 10 in the answer...up to a certain point. Assuming you use 3.14 for the odd (or leftover) factors of π, here would be your estimations: