Upload
trinhnguyet
View
217
Download
0
Embed Size (px)
Citation preview
A property that can be measured and described by a number and a unit
Numbers without units are useless!
A Quantity is…
Descriptions of quantities such as length, mass, or temperature
Ex. 3.54cm
Cannot be exact values
Exact numbers = no uncertainty
Ex. 4 people (there cannot be 4.25 people)
What are measurements?
Accuracy: how close the measured value is to what it should be (the actual value)
Precision: how reproducible the measurement is
can you get the same value over and over again?
Accuracy vs. Precision
if a measurement is precise, but not accurate there is a systematic error or bias
Ex. you get the same wrong answer over and over
if a measurement is accurate but not precise, experimenter is being inconsistent
indicate the precision and accuracy of a measured value
the last significant figure in any measurement is uncertain (it was estimated/rounded/etc.)
all other numbers are certain
Ex. 8.658m
8.65 are certain numbers
last 8 is uncertain
could be 8.657m or 8.659m
Significant Figures (aka. Sig figs):
accuracy is shown by the number of significant figures
Ex. 526 is more accurate than 530
precision is shown by the place value of the number
the less uncertainty, the greater the precision
the more sig.figs you have, the less uncertainty and greater precision
Ex. 526.45789563 is more precise than 526.5
Ex.
Student A 34.94 g, 35.01 g, 35.07 g
Student B 34.98 g, 34.96 g, 34.97 g
Student C 35.01 g, 34.99 g, 35.03 g
Exact mass of the beaker is 35.02 grams
Who was the most accurate? C Who was the most precise? B
Who was the least accurate? B
Who was the least precise? A
1. All non-zero digits are significant regardless of the position of the decimal point
Ex. 8.658m = 4 sig figs
2. In the absence of a decimal point, zeros at the end of a number are not significant
Ex. 1990g = 3 sig figs
3. Zeros are significant at the end of a number with a decimal place
Ex. 1990.g = 4 sig figs
Sig Fig Rules:
4. All zeros between significant figures are significant
Ex. 1205 = 4 sig figs
5. Zeros at the beginning of a number are not significant
Ex. 0.0023 = 2 sig figs
How many significant figures are in each of the following:
a) 21.35 4
b) 8.005 4
c) 121.2000 7
d) 0.000823 3
e) 0.0980 3
f) 38,020 4
Reminder: starts with a non-zero digit which may be followed by a decimal and other digits
first # 1< x < 10
all digits in scientific notation are significant
Ex. 1990g = 1.99x103g
Ex. Write in scientific notation:
1. 863,000,000 8.63 x 108
2. 0.000009357 9.357 x 10-6
Convert to decimal form:
1. 4.261 x 105 426100
2. 8.47 x 10-6 0.00000847
Scientific Notation and Sig Figs
Math with Significant Figures:
Addition/ Subtraction Rule: round to the least precise place of the
starting values
Ex. 3.05 + 1.0004 = 4.05
Multiplication/ Division Rule: round to the least number of significant
figures of the starting values
Ex. (9.00005 x 3.1) = 7
4
When addition / subtraction and multiplication / division appear in the same calculation…
1.Follow the order of operations rules (BEDMAS) finding the correct sig figs at each step
2.Round your final answer to the correct number of significant figures
Mixed calculations?
NOTE : DO NOT ROUND until your final answer, just keep track of how many significant figures your answer should have…or else it could change your answer
WARNING:
Reading a Scale!
Remember in all measurements the last number is uncertain…that is because…
the last digit is always estimated (between the smallest division)
Ex. 42.6mL would have 2 certain digits (4, 2) and 1 uncertain digit (6)
Uncertainty in Measurements: The uncertainty is always in the last digit
(the one that was estimated)
This can be expressed as part of the number
Uncertainty is 1/10 of the smallest division on the instrument
Ex. 42.6 + 0.1mL
uncertainty term
Range = 42.5mL to 42.7mL