Accuracy and Precision Section 3 Using Scientific Measurements Chapter 2 Accuracy and Precision Accuracy - closeness of measurements to the correct or accepted value of the quantity measured. Precision - closeness of a set of measurements of the same quantity made in the same way.

Accuracy and Precision Section 3 Using Scientific Measurements Chapter 2 Accuracy and Precision

Section 3 Using Scientific Measurements Chapter 2 Percentage error – percentage a measurement is off from the accepted value

Chapter 2 Sample Problem C Section 3 Using Scientific Measurements Chapter 2 Sample Problem C A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percentage error of the student’s measurement?

Chapter 2 Error in Measurement Section 3 Using Scientific Measurements Chapter 2 Error in Measurement Some error or uncertainty always exists in any measurement. skill of the measurer conditions of measurement measuring instruments

Section 3 Using Scientific Measurements Chapter 2 Significant figures - consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. The term significant does not mean certain.

Reporting Measurements Using Significant Figures Section 3 Using Scientific Measurements Chapter 2 Reporting Measurements Using Significant Figures

Chapter 2 Determining the Number of Significant Figures Section 3 Using Scientific Measurements Chapter 2 Determining the Number of Significant Figures

Chapter 2 Sample Problem D Section 3 Using Scientific Measurements Chapter 2 Sample Problem D How many significant figures are in each of the following measurements? a. 28.6 g b. 3440. cm c. 910 m d. 0.046 04 L e. 0.006 700 0 kg

Chapter 2 Significant Figures Rounding Section 3 Using Scientific Measurements Chapter 2 Significant Figures Rounding

Chapter 2 Addition or Subtraction with Significant Figures Section 3 Using Scientific Measurements Chapter 2 Addition or Subtraction with Significant Figures Least precise place value Multiplication or Division with Significant Figures Least total significant figures

Section 3 Using Scientific Measurements Chapter 2 Addition or Subtraction with Significant Figures 15.78 g + 3.1 g Answer will go by lowest placeholder. Multiplication or Division with Significant Figures Answer will have the same as the least total significant figures. 15.78 g x 3.1 g

Chapter 2 Sample Problem E Section 3 Using Scientific Measurements Chapter 2 Sample Problem E Carry out the following calculations. Express each answer to the correct number of significant figures. a. 5.44 m - 2.6103 m b. 2.4 g/mL  15.82 mL

Chapter 2 Conversion Factors and Significant Figures Section 3 Using Scientific Measurements Chapter 2 Conversion Factors and Significant Figures Disregard conversion factors when determining significant figures.

Section 3 Using Scientific Measurements Chapter 2 Scientific notation - numbers are written in the form M  10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number. example: 0.000 12 mm = 1.2  104 mm

Chapter 2 Scientific Notation Convert into scientific notation: Section 3 Using Scientific Measurements Chapter 2 Scientific Notation Convert into scientific notation: 47,532 g 0.0029 m 583.4 s

Chapter 2 Mathematical Operations Using Scientific Notation Section 3 Using Scientific Measurements Chapter 2 Mathematical Operations Using Scientific Notation 1. Addition and subtraction —These operations can be performed only if the values have the same exponent (n factor). example: 4.2  104 kg + 7.9  103 kg or

Chapter 2 Mathematical Operations Using Scientific Notation Section 3 Using Scientific Measurements Chapter 2 Mathematical Operations Using Scientific Notation 2. Multiplication —The M factors are multiplied, and the exponents are added algebraically. example: (5.23  106 µm)(7.1  102 µm) = (5.23  7.1)(106  102) = 37.133  104 µm2 = 3.7  105 µm2

Chapter 2 Mathematical Operations Using Scientific Notation Section 3 Using Scientific Measurements Chapter 2 Mathematical Operations Using Scientific Notation 3. Division — The M factors are divided, and the exponent of the denominator is subtracted from that of the numerator. example: = 0.6716049383  103 = 6.7  102 g/mol

Chapter 2 Sample Problem F Section 3 Using Scientific Measurements Chapter 2 Sample Problem F Calculate the volume of a sample of aluminum that has a mass of 3.057 kg. The density of aluminum is 2.70 g/cm3.

Chapter 2 Direct Proportions Section 3 Using Scientific Measurements Chapter 2 Direct Proportions Two quantities are directly proportional to each other if dividing one by the other gives a constant value.

Section 3 Using Scientific Measurements Chapter 2 Direct Proportion

Chapter 2 Inverse Proportions Section 3 Using Scientific Measurements Chapter 2 Inverse Proportions Two quantities are inversely proportional to each other if their product is constant.

Section 3 Using Scientific Measurements Chapter 2 Inverse Proportion