What are the Differences Between Qualitative and Quantitative Measurement?
Qualitative Measurement – gives results in a descriptive, nonnumerical form
Describes a quality
Examples: object is hot, the person is tall, tractors are big, the surface is smooth
Quantitative Measurement
Quantitative Measurement - gives results in a definite form, usually as numbers and units
Describes a quantity
Examples: water is 100.0 oC, the person is 1.2 m tall, the tractor’s mass is 4.00x103 kg, the volume of the cube is 7.5 cm3
What is the Difference Between Accuracy and Precision?
Accuracy – measure of how close a measurement comes to the actual or true value of whatever is measured
Example: hitting the bull’s-eye on a dartboard
Precision
Measure of how close a series of measurements are to one another
Quality of measurements
Example: hitting roughly the same spot on a dartboard several times
Precision and Measurements
How precise a measurement is depends on the tool used to make the measurement.
Precision is determined by the number of quantitative markers on the measuring tool.
We always measure / estimate to one decimal place beyond the tool’s marks.
Error Calculations
ERROR =
experimental value – accepted value
Magnitude of the value tells whether or not the experimental value is too high or too low
Error Calculations
Accepted value: Accurate value based on a reliable reference
Experimental value: value measured in lab
Percent Error = | Error | x 100%
Accepted Value
Example:
Sulfur melts at 113.0 oC. In a lab, you measure the temperature at which sulfur melts to be 110.7 oC. What is the error and percent error in this measurement?
Remember:
Percent Error = | Error | x 100%
Accepted Value
Example:
Sulfur melts at 113.0 oC. In a lab, you measure the temperature at which sulfur melts to be 110.7 oC. What is the error and percent error in this measurement?
Percent Error = | 110.7 – 113.0 | x 100%
113.0
Example:
Sulfur melts at 113.0 oC. In a lab, you measure the temperature at which sulfur melts to be 110.7 oC. What is the error and percent error in this measurement?
Percent Error = 2.035%
Scientific Notation
Scientific Notation – a number written as the product of two numbers: a coeffiecient and 10 raised to a power
Examples:
6,200 = 6.2 x 103
0.0062 = 6.2 x 10-3
Multiplication:
Multiplication – multiply the coefficients and add exponents
Example:
(2.0 x 102) x (5.0 x 103)
= (2.0 x 5.0) x 10(2+3)
= 10 x 105 = 1.0 x 106
Division:
Division – divide coefficients and subtract exponent in denominator from exponent in numerator
Example:
2.0 x 102 ÷ 5.0 x 103
= (2.0 ÷ 5.0) x 10(2-3)
= 0.4 x 10-1 = 4.0 x 10-2
Addition and Subtraction:
Make sure exponents are the same
Add or subtract number
Example: (6.2 x 103) + (2.0 x 102)
6.2 x 103
+ 0.2 x 103
6.4 x 103
Solve the following:
Convert the following numbers into scientific notation:
530,000 =
0.023 =
44 =
123,450,000 =
0.000098 =
Solve the following:
Convert the following numbers into scientific notation:
530,000 = 5.3 x 105
0.023 = 2.3 x 10-2
44 = 4.4 x 101
123,450,000 = 1.2345 x 108
0.000098 = 9.8 x 10-5
Perform the following calculations:
(2.0 x 103) x (4.3 x 102) =
(3.4 x 106) / (4.1 x 104) =
(5.66 x 104) + (2.1 x 103) =
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