What is the value of $142,857 \times 7^2$? 
What is the value of $142,857 \times 7^2$?

Obviously you could solve this with a calculator and be done. But is there a more clever way to calculate this?

If you recognize that those are the decimal digits of $1/7 = .142857142857142857...$, then you realize that $1000000/7$ must be 142857+0.142857, so 142857 must be (100,000 - 1)/7, and you're on your way. 
