Unit 1- Units and Measurement
Chemistry
Scientific Notation, Measurement, Accuracy, Precision, Error
Scientific Notation
M x 10n
M is the coefficient 1<M<10 10 is the base n is the exponent or power of 10 n is positive if number is greater 1 n is negative if number is less 1
Scientific Notation Write the following in scientific notation:
5450000 =
0.0002570 =
Limits of Measurement
Accuracy and PrecisionUncertaintyExact Numbers vs. Inexact
Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.
Example: AccuracyWho is more accurate when
measuring a book that has a true length of 17.0cm?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm
Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.
Example: Precision
Who is more precise when measuring the same 17.0cm book?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm
Example: Evaluate whether the following are precise, accurate or both.
Error
Error= experimental –accepted value
Percent Error
% Error= |experimental –accepted| x100
accepted value
Significant Figures
The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.
Uncertainty-
Centimeters and Millimeters
The last (farthest to the right) significant figure in a measured quantity alwayshas some associated uncertainty. The minimum uncertainty is ± 1 in the last digit
Graduated Cylinder - Meniscus
Reading Scales to the Correct Significant Figures Uncertainty?
Reading Scales to Correct Significant Figures
Reading Scales to Correct Significant Figures Uncertainty?
Rules for Counting Significant Figures
All nonzero digits are significant. (42 has 2 sf’s.) Zeros in the middle of a number are significant. (4.803 cm has 4 sf’s.) Leading zeros are not significant; they are there to locate the decimal point. (0.00123 g has three sf’s.) Trailing zeros are significant if the number contains a decimal point. (55.220 K has five sf’s; 50.0 mg has three sf’s, 5.100 × 10-3 has four sf’s.) Trailing zeros are not significant if the number does not contain a decimal. (34,200 m has three sf’s.)
How many sig figs?100 kg 0.000303 mm
10302.00 cm 92,900,000 km
0.001L 6.02 x 1023 atoms
10302 m 0.0205 m
1.0302x104 ms2.05 x 10-2 m
1010.010 g
Sig Figs in Addition/Subtraction
The result has the same number of decimal places as the number in the operation with the least decimal places.
Ex: 2.33 cm
+3.0 cm
5.3 cm
Sig Figs in Multiplication/Division
The answer has the same sig figs as the factor with the least sig figs.
Ex: 3.22 cm
x 2.0 cm
6.4 cm2
Measured Numbers vs. Exact Numbers Exact numbers are values that are known
exactly (3 atoms = 3.00000…atoms) or that are true by definition: 12 inches = 1foot, 60 s = 1 min, 5280 feet = 1 mile, 100 cm = 1m, 2.54 cm = 1 inch, etc.
All inexact or measured numbers will have some limit to how precisely they are known, and there is a limit to the number of significant digits contained in the number.