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Scientific Measurements. Know the difference between exact and measured quantities or numbers. Know the difference between precise and accurate measurements. Indicate whether a given data set is precise, accurate, both, both or neither.
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Scientific Measurements • Know the difference between exact and measured quantities or numbers. • Know the difference between precise and accurate measurements. • Indicate whether a given data set is precise, accurate, both, both or neither. • Know how to express the degree of precision with the correct number of significant figures, and indicate the uncertainty in the number.
Know how to express a number in scientific notation. • Convert any number in normal notation to scientific notation, and vice versa. • Express any number written in scientific notation as a number with a different power of ten (e.g., 1.23 x 105 = 123 x 103).
Significant Figures • Whenever a number is obtained from a measurement, there will be some uncertainty • Significant figures (or sig figs) are the ones that are not beyond the accuracy of the measuring device.
Important conventions • 1. The last place in the number is where the uncertainty lies. • 2. The uncertainty is +/- 1 of these units. • Example: in 30.6 cm, the uncertainty is +/- 0.1 (since the last place is the tenths place).
Rounding off • To write a numerical answer with the proper number of significant figures, we often have to round off numbers. In rounding, we drop all digits that are not significant, and if necessary, adjust the last reported digit.
Rounding off conventions • If the leftmost digit to be dropped is 0, 1, 2, 3, 4, leave the final remaining digit unchanged. • Example: 369.442 rounds to 369.44 if we need five sig figs. • If the leftmost digit to be dropped is 5, 6, 7, 8, 9, increase the final remaining digit by one. • Example: 538.768 rounds to 538.77 if we need five sig figs.
All non-zero digits in a number are significant; they are the result of measurement. • But zeros may be the result of a measurement or they may simply be used to indicate the size of the result.
a. The zeros in 0.00274 are not significant digits. • b. All of the zeros in 204.50 are significant. • c. The zeros in 34,000 may or may not be significant;
Sig Figs in Products and Quotients • There are no more significant figures in a product or a quotient than in the data with the fewest number of significant figures.
Sig Figs in Differences and Sums • The result has the same number of digits to the right of the decimal point as the term with the fewest digits to the right of its decimal point. Thus, the term with the lowest absolute precision determines the precision of the result.