1. ROUNDING OFF PROCEDURES Getting rid of extra digits the right way…

2. Why round? We round to correctly represent the precision of a calculation that is based on measurements. The precision of each measurement is determined by the accuracy of the instrument used.

3. Round Down… …whenever the last significant digit is followed by 0, 1, 2, 3 or 4: 30.24 becomes 30.2 …whenever the last significant figure is even, followed by a 5 with no other digits: 32.25 becomes 32.2 (but 32.250 is 32.3)

4. Round Up… …whenever the last significant digit is followed by 6, 7, 8 or 9: 30.49 becomes 30.5 …whenever the last significant figure is odd, followed by a 5 with no other digits: 32.35 becomes 32.4 …if the digit following the last significant figure is a 5 followed by any digits: 32.50, 32.54, 32.57 and 32.59 all become 32.6

5. Simplified Procedure Round down when the last significant figure is followed by 0, 1, 2, 3 or 4. Round up when the last significant figure is followed by 5, 6, 7, 8 or 9. down:up: 0 to 45 to 9

6. Rounding vs. Truncating When rounding, we adjust the last digit to correctly represent the precision of the calculation. This means we can adjust it up or down, depending on the following digits. Ex: 0.3257 is 0.326; 1.24 is 1.2 When truncating, we drop the non-significant digits, regardless of what they are. It is like “rounding down” every time. Ex: 0.3257 is 0.325; 1.24 is 1.2 Some calculations require a truncated answer to make sense. (Ex: book, p. 28, # 12)

7. THE END Lilian Wehner ©