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# Chapter 2.3 : Using Scientific Method

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• 1. Using scientific measurements
SECTION 2-3
• 2. 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
• 3. 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.
• 4. 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
• 5. Error in Measurement
Observer
Equipment
Conditions
• 6. Significant Figures
Consists of all digits know with certainty, plus one final digit
• 7. 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.
• 8. 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
• 9. 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
• 10. 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.
• 11. 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
• 12. Scientific Notation
Extremely small numbers – negative exponent
Ex: 0.0000000000567 g
5.67 x 10-11 g
M should be in significant figures
• 4.2 x 104 + 7.9 x 103 =
• 13. 5.o x 104
• Direct Proportions
Two quantities if divided by the other gives a constant value
If one doubles so does the other
y = kx
• 14. Inverse Proportions
Two quantities who’s product is a constant
If one doubles, the other is cut in half
xy = k