Physics: estimates

Tutoring physics, approximations often help. The tutor mentions a comparison between exact and approximate.

Example 1: Imagine a projectile launched according to the equation
h=-4.9t^2 +22t + 15 What would be its height at 3.0 seconds?

Solution: h=-4.9(3.0)^2+22(3.0)+15=36.9m or 37m (sig digs)

Yet, for an approximate height, h=-5.0(3.0)^2+22(3.0)+15=36m

36m is 1/37, or 2.7% different from the exact answer. It gives a very helpful guide towards what to expect from the true answer. Moreover, using -5.0 instead of -4.9, the approximate answer is relatively easy to produce mentally.

Knowing very close to what the answer will be is helpful. Then, if a wrong keystroke is made calculating the exact answer, the student will be aware and try again.