Slide1: Significant Figures Significant figures in a measurement 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. Section 3 Using Scientific Measurements Chapter 2
Reporting Measurements Using Significant Figures: Reporting Measurements Using Significant Figures Section 3 Using Scientific Measurements Chapter 2
Slide3: Significant Figures, continued
Determining the Number of Significant Figures Section 3 Using Scientific Measurements Chapter 2
Significant Figures, continued: Significant Figures, continued 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 Section 3 Using Scientific Measurements Chapter 2 For these examples:
A=1, B=2, C=3, D=4, E=5
Significant Figures, continued: a. 28.6 g Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued Sample Problem D Solution
By rule 4, the zero is not significant; there are 2 significant figures.
c. 910 m
By rule 4, the zero is significant because it is immediately followed by a decimal point; there are 4 significant figures.
b. 3440. cm
There are no zeros, so all three digits are significant.
Significant Figures, continued: d. 0.046 04 L Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued Sample Problem D Solution, continued
By rule 2, the first three zeros are not significant; by rule 3, the last three zeros are significant; there are 5 significant figures.
e. 0.006 700 0 kg By rule 2, the first two zeros are not significant; by rule 1, the third zero is significant; there are 4 significant figures.
Slide7: Significant Figures, continued
Addition or Subtraction with Significant Figures When adding or subtracting decimals, 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. Multiplication or Division with Significant Figures For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. Section 3 Using Scientific Measurements Chapter 2
Significant Figures, continued: 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 Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued
Significant Figures, continued: Sample Problem E Solution
a. 5.44 m - 2.6103 m = 2.84 m Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued
There should be two significant figures in the answer, to match 2.4 g/mL.
There should be two digits to the right of the decimal point, to match 5.44 m.
b. 2.4 g/mL 15.82 mL = 38 g
Slide11: Scientific Notation In 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. Section 3 Using Scientific Measurements Chapter 2
Move the decimal point four places to the right, and multiply the number by 104. example: 0.000 12 mm = 1.2 104 mm
Slide12: Scientific Notation, continued
Mathematical Operations Using Scientific Notation 1. Addition and subtraction —These operations can be performed only if the values have the same exponent (n factor). VERY IMPORTANT!!!!
example: 4.2 104 kg + 7.9 103 kg or Section 3 Using Scientific Measurements Chapter 2
Slide13: 2. Multiplication —The M factors are multiplied, and the exponents are added algebraically. Section 3 Using Scientific Measurements Chapter 2 Scientific Notation, continued
Mathematical Operations Using Scientific Notation
= 3.7 105 µm2
= 37.133 104 µm2
= (5.23 7.1)(106 102)
example: (5.23 106 µm)(7.1 102 µm)
Slide14: 3. Division — The M factors are divided, and the exponent of the denominator is subtracted from that of the numerator. Section 3 Using Scientific Measurements Chapter 2 Scientific Notation, continued
Mathematical Operations Using Scientific Notation = 0.6716049383 103
= 6.7 102 g/mol
example: