Rounding the Answer

Rounding keeps the digits asked for and looks at the next one: 5 or more rounds up, 4 or less leaves the last kept digit alone. A side of 20 cos 65° is 8.45236... To one decimal place that is 8.5 (the next digit, 5, rounds up). To three places it is 8.452 (the next digit, 3, leaves it).

Round once, at the very end. If you round cos(65°) to 0.42 first, 20 × 0.42 gives 8.40, and the answer is already wrong in the second decimal. The board keeps x = 20cos(65°) exact until you press the round chip, so the digits it keeps are the true ones.

The lesson's places are part of the answer. There is no tolerance: to three places, 8.452 is right and 8.45 or 8.4524 is not.