Unit 2 – Qualitative and Quantitative Measurements (3.1)

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

3.1 –Uncertainty in Measurement

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.

What can/should we record as the

length of the object?

What can/should we record as the

length of the object? 3.15 cm

What can/should we record as the

length of the object?

What can/should we record as the

length of the object? 1.52 cm

What can / should we record as

the volume in this graduated

cylinder?

What can / should we record as

the volume in this graduated

cylinder? 36.5 mL

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%

Unit 2 – Review of Scientific Notation (3.1)

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) =

Perform the following calculations:

(2.0 x 103) x (4.3 x 102) = 8.6 x 105

(3.4 x 106) / (4.1 x 104) = 8.29 x 101

(5.66 x 104) + (2.1 x 103) = 5.87 x 104