What is the best estimate for the product of 289 and 7

The best estimate is 2100.

Because 289 rounded to the nearest hundredth is 300, and by using simple time tables (3 * 7 = 21), we can determine that 300 * 7 = 2100.

But if you want an even closer estimate, do this:

(200 * 7) + (90 * 7) = (1400) + (630) = 2030.

And to get the exact answer...

(200 * 7) + (80 * 7) + (9 * 7) = (1400) + (560) + (63) = (1960) + (63) = 2023.

2032 is the exact answer. The two solutions above involve the usage of time tables and place-value manipulation - (ab) * c = a*c + b*c, in which ab represents a 2 digit number)