Objectives Distinguish between accuracy and precision Determine the number of significant figures in measurements Perform mathematical operations involving significant figures Convert measurements into scientific notation Distinguish between inversely and directly proportional relationships
Accuracy and Precision Accuracy – the closeness of measurements to the correct or accepted value of the quantity measured Precision – the closeness of a set of measurements of the same quantity made in the same way.
Percent Error Calculated by subtracting the experimental value from the accepted value, dividing the difference by the accepted value, and then multiplying by 100 Percent error = valueaccepted - valueexperimental x 100 valueaccepted
Error in Measurement Observer Equipment Conditions
Significant Figures Consists of all digits know with certainty, plus one final digit
Rules for determining significant zeros Digits from 1-9 are always significant. Zeros between two other significant digits are always significant One or more additional zeros to the right of both the decimal place and another significant digit are significant. Zeros used solely for spacing the decimal point (placeholders) are not significant.
Rounding Greater than 5 inc. by 1 42.68 42.7 Less than 5 stay 17.32 17.3 5, followed by nonzero inc. by 1 2.7851 2.79 5, not followed by nonzero inc. by 1 4.635 4.64 Preceded by odd digit 5, not followed by nonzero stays 78.65 78.6 Preceded by Even digit
Addition/subtraction with significant figures The answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. 35. 1 + 2.3456 37.4456 So : 37.4
Multiplication/Division with significant figures The answer can have no more significant figures than are in the measurement with the fewest number of significant figures. 3.05 g ÷ 8.470 mL = 0.360094451 g/mL 3 s.f. 4 s.f. Should be 3 s.f.
Scientific Notation Numbers are written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number. 65 ooo km M is 6.5 Decimal moved 4 places to left X 104 So: 6.5 x 104 km Why? Makes very small or large numbers more workable 60 200 000 000 000 000 000 000 molecules 6.02 x 1023 molecules
Scientific Notation Extremely small numbers – negative exponent Ex: 0.0000000000567 g 5.67 x 10-11 g M should be in significant figures