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Learning Objectives. Give an example of a measurement whose number of significant digits is clearly too great, and explain why. State the purpose of rounding off, and describe the information that must be known to do it properly. Round off a number to a specified number of significant digits.
Before dealing with the specifics of the rules for determining the significant figures in a calculated result, we need to be able to round numbers correctly. To round a number, first decide how many significant figures the number should have.
When you round off, you change the value of the number, except if you round off a zero. Following the old rules, you can round a number down in value four times (rounding with one, two, three, four) compared to rounding it upwards five times (five, six, seven, eight, nine).
Define accuracy and precision; Distinguish exact and uncertain numbers; Correctly represent uncertainty in quantities using significant figures; Apply proper rounding rules to computed quantities
Significant figures, also referred to as significant digits or sig figs, are specific digits within a number written in positional notation that carry both reliability and necessity in conveying a particular quantity.
The rules for deciding the number of significant figures are: Non-zero digits are significant unless indicated otherwise (for instance see 8. below). Zeros between two non-zero digits are significant. Zeros before the first non-zero digit (i.e. “leading zeros”) are not significant (for instance 0.003 has only one significant figure).
Rounding Rules. Identify the first digit to be dropped (immediately to the right of the last significant figure). If it is: less than 5 (0, 1, 2, 3, or 4), then leave the last significant figure unchanged (round down) example: rounding 52.51 to three significant figures becomes 52.5.
