Unit 1 Part 1: Significant Figures and Scientific Notation. Objective understand significant figures and their rules. Be able to use scientific

Transcription

1 Unit 1 Part 1: Significant Figures and Scientific Notation. Objective understand significant figures and their rules. Be able to use scientific notation in calculations.

2 Significant figures - consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.

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4 Rule 1 - Zeros appearing between nonzero digits are significant. How many significant figures in the following? L? ,009 km? 5

5 Rule 2 - zeros appearing in front of nonzero digits are not significant. How many significant figures in the following? m? kg? 1

6 Rule 3 - zeros at the end of a number and to the right of a decimal are significant. How many significant figures in the following? g? mm? 7

7 Rule 4 - if a zero is a placeholder, it is not significant. If there is a decimal after the zero, it is significant. How many significant figures in the following? m? m? 4

8 Significant Figures, continued How many significant figures are in each of the following measurements? a g b cm c. 910 m d L e kg

9 Significant Figures, continued a g There are no zeros, so all three digits are significant. b cm The zero is significant because it is immediately followed by a decimal point; there are 4 significant figures. c. 910 m The zero is not significant; there are 2 significant figures.

10 Significant Figures, continued d L The first two zeros are not significant; the third zero is significant; there are 4 significant figures. e kg The first three zeros are not significant; the last three zeros are significant; there are 5 significant figures.

11 Significant Figures Practice x , x 10-9

12 Significant Figures Practice = = x 10-5 = ,600 = x 10-9 = 4

13 Significant Figures Practice ,000

14 Significant Figures, continued 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. Example: a m m =

15 Significant Figures, continued 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. Example: a m m = 2.84 m There should be two digits to the right of the decimal point, to match 5.44 m.

16 Significant Figures, continued Multiplication or division - the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. Example: 2.5 x 3.42 = - Provide the answer to the problem and how many significant figures you would include.

17 Significant Figures, continued Multiplication or division - the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. Example: 2.5 x 3.42 = 8.6 (rounded from the calculator reading of 8.55). 2.5 has two significant figures while 3.42 has three.

18 Unit Conversion Example 1: Convert 4800 g to kg

19 Unit Conversion Example 2: Convert 245 ms to s

20 Unit Conversion Example 3: Mass: 3000 kg Volume: 1000 cm 3 Find the density:

21 Practice Problems (use p.35 for help) grams to milligrams centimeters to meters kilograms to grams millimeters to meters meters to centimeters m x 2.09m = ft 2 / 1.07 ft 2 = x 3.5 = = =

22 Scientific notation In scientific notation, numbers are written in the form M 10 n M is a number greater than or equal to 1 but less than 10. While, n is a whole number example: mm = mm Move the decimal point four places to the right and multiply the number by 10 4.

23 Scientific notation Addition and subtraction These operations can be performed only if the values have the same exponent (n factor). example: kg kg

24 Scientific notation Addition and subtraction These operations can be performed only if the values have the same exponent (n factor). example: kg kg

25 Scientific notation Multiplication The M factors are multiplied, and the exponents are added algebraically. example: ( m)( m) = ( )( ) = m 2 = m 2

26 Scientific notation Division The M factors are divided, and the exponent of the denominator is subtracted from that of the numerator. example:

27 Scientific notation Division The M factors are divided, and the exponent of the denominator is subtracted from that of the numerator. example: = = g/mol

28 Sample Problems Calculate the volume of a sample of aluminum. Mass of aluminum = kg. Density of aluminum = 2.70 g/cm 3. Check the units. Conversion factor: 1000 g = 1 kg Rearrange the density equation to solve for volume.

29 Convert kg to proper units kg x 1000 g = 3057 g 1 kg Next, divide by the density to solve for volume V = 3057 g = cm 3 (calculator answer) 2.70 g/cm 3 Round answer to three significant figures V = cm 3

30 Practice Problems Modern Chem P.57 # g g m x 6.41 m g / ml 4. (1.54 x 10-2 g) + (2.86 x 10-1 g) 5. (7.023 x 10 9 g) (6.62 x 10 7 g) 6. (8.99 x 10-4 m) x (3.57 x 10 4 m) 7. (2.17 x 10-3 g) / x 10 4 ml) ,000 and 33,400 and in scientific notation x x ( x 10 7 ) (5.61 x 10-4 )