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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.
- Significant Figures in Calculations
Before dealing with the specifics of the rules for...
- Significant Figures in Calculations
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.
Rules for rounding off numbers (1) If the digit to be dropped is greater than 5, the last retained digit is increased by one. For example, 12.6 is rounded to 13. (2) If the digit to be dropped is less than 5, the last remaining digit is left as it is. For example, 12.4 is rounded to 12.
What are Sig Figs? Significant figures relay the number of digits reliably known in a number. Measured quantities are typically reported such that only the last significant digit is uncertain. There are a few important rules for determining which digits in a given number are significant: Non-zero numbers are ALWAYS significant.
There are three rules on determining how many significant figures are in a number: Non-zero digits are always significant. Any zeros between two significant digits are significant. A final zero or trailing zeros in the decimal portion ONLY are significant. Focus on these rules and learn them well.
The rules for deciding the number of significant figures are: 1. Non-zero digits are significant unless indicated otherwise (for instance see 8. below). 2. Zeros between two non-zero digits are significant. 3. Zeros before the first non-zero digit (i.e. “leading zeros”) are not significant (for instance 0.003 has only one significant figure ...
The following rules dictate the manner in which numbers are to be rounded to the number of figures indicated. The first two rules are more-or-less the old ones. Rule three is the change in the old way. When rounding, examine the figure following (i.e., to the right of) the figure that is to be last.
