MEASUREMENT(A Quantitative Observation)
• MEASUREMENTS always have 2 things:
Number & Unit
• All measurements have error in them!
• A measurement consists of all known digits that can be known accurately PLUS one digit that is ESTIMATED.
• The estimated digit is always at the END of the number in a measurement.
MEASUREMENT& Degrees of Error
• The closer a measurement is to the true value, the more accurate the measurement.
• Accurate measurements are “more correct” and closer to the true value.
• Accuracy = Correctness.• How close a series of measurements are to one
another is called precision.• Precise measurements are close in value to one
another; repeated measures are precise. • Precision = Reproducibility.
Accuracy vs. Precision
• Another example: a 5 lb bag of potatoes is weighed by 3 people, 3 times each.
Person 1
4.9 lbs
4.8 lbs
4.85 lbs
Person 2
4.0 lbs
3.5 lbs
5 lbs
Person 3
4.0 lbs
4.1 lbs
4.2 lbs
Good Accuracy
Good Precision
Poor Accuracy
Poor Precision
Poor Accuracy
Good Precision
Determining Error• Accepted value is the correct value based
on reliable references.
• Reference: boiling point of water is 100.0°C
• Experimental value: temperature of boiling water measured to be 99.1°C
• ERROR = experimental – accepted value
• ERROR = (99.1°C – 100.0 °C) = –0.9 °C• (-) means your measurement was less
than the number of the true value. • (+) means your measurement is greater
than the true value.• PERCENT ERROR is an absolute value:
• %ERROR = (0.9/100) x 100 = 0.9%
100% accepted
errorerror
A way to express very large or very small numbers easily.
Example:
.0000000000000036333 seconds
= 3.6333 x 10-15 seconds
= 9.8765 x 1012 minutes
9876500000000 minutes
SCIENTIFIC NOTATION
Practice
(1) .000565 g 5.65 x 10-4 g
(2) 565000 s
5.65 x 105 s
(3) 43454 min
4.3454 x 104 min(4) .0010 L 1.0 x 10-3 L
Measurement Limitations
• ALL measurements have error in them!• A measurement consists of all known digits that
can be known accurately PLUS one digit that is estimated.
• The estimated digit is always at the end of the number in a measurement.
• All of the digits that are known in a measurement are significant figures.
• Fewer significant figures = more rounding in a measurement = more error.
What are the following lengths (in meters)?
(A)
(B)
(C)
ANSWERS
(A) 0.3 m (1 decimal place)
(B) 0.26 m (2 decimal places)
(C) 0.260 m (3 decimal places)
What is the density of a sample with a mass of 24.47 g and a volume of 13.2 mL?
A. 1.9 g/mL B. 1.8537 g/mL C. 1.854 g/mL D. 1.85 g/mL
APPLYING SIG FIGS to MEASUREMENT:
HINT: Your FINAL answer cannot be more accurate than the least accurate measurement.
What is the density of a sample with a mass of 24.47 g and a volume of 13.2 mL?
A. 1.9 g/mL B. 1.8537 g/mL C. 1.854 g/mL D. 1.85 g/mL
APPLYING SIG FIGS to MEASUREMENT:
Because 13.2 mL is accurate to only one decimal place, the answer can be no more accurate than one decimal place.
Easy Rules To Sig Figs
• ALL trailing zeros in a non-decimal are NOT significant (they act as placeholders only)
• ALL leading zeros in a decimal are NOT significant (they act as placeholders only)
• Sandwhiched zeros count (i.e. 101, 0.101)
• In a decimal, if the zero in question has a number 1 thru 9 before it anywhere in the number, it is significant! (i.e. 0.000000100000)
Putting It ALL Putting It ALL TogetherTogether
the speed of light = 299 792 458 m / s9 significant figures (sig figs)2.99 792 458 x 108 m/s8 sig figs = 2.99 792 46 x 108 m/s7 sig figs = 2.99 792 5 x 108 m/s6 sig figs = 2.99 792 x 108 m/s5 sig figs = 2.99 79 x 108 m/s4 sig figs = 2.99 8 x 108 m/s3 sig figs = 3.00 x 108 m/s2 sig figs = 3.0 x 108 m/s1 sig figs = 3 x 108 m/s
ROUNDING 123 456 789
• 123456790• 123456800• 123457000• 123460000• 123500000• 123000000• 120000000• 100000000
= 1.2345679 x 108
= 1.234568 x 108
= 1.23457 x 108 = 1.2346 x 108
= 1.235 x 108
= 1.23 x 108
= 1.2 x 108
= 1 x 108
Determine the Significant Figures• 1.0 blah
• 100000000.0 blah
• 100 blah
• 100. blah
• 0.10 blah
• 0.01 blah
• 0.010 blah
• 101 blah
Answers• 1.0 blah 2 sig figs
• 100000000.0 blah 10 sig figs
• 100 blah 1 sig fig
• 100. blah 3 sig figs
• 0.10 blah 2 sig figs
• 0.01 blah 1 sig fig
• 0.010 blah 2 sig figs
• 101 blah 3 sig figs
Answers in Scientific Notation• 1.0 x 100 blah 2 sig figs
• 1.000000000 x 108 blah 10 sig figs
• 1 x 102 blah 1 sig fig
• 1.00 x 102 blah 3 sig figs
• 1.0 x 10-1 blah 2 sig figs
• 1 x 10-2 blah 1 sig fig
• 1.0 x 10-2 blah 2 sig figs
• 1.01 x 102 blah 3 sig figs
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