sample problem
DESCRIPTION
Sample Problem. A typical bacterium has a mass of about 2.0 fg. Express this measurement in terms of grams and kilograms. Step 1. Write what we know . . . then what we are looking for. Unknown: mass = ? g mass = ? kg. Given: mass = 2.0 fg. Sample Problem. Step 2. - PowerPoint PPT PresentationTRANSCRIPT
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Sample ProblemA typical bacterium has a mass of about 2.0 fg. Express this measurement in terms of grams and kilograms.
Unknown: mass = ? g
mass = ? kg
Given: mass = 2.0 fg
Write what we know . . . then what we are looking for.Step 1
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Step 2
–15
–15
1 10 g 1 fg and
1 fg 1 10 g
Sample Problem
These fractions equal 1, since the numerator and the denominator are equal by conversion
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Step 3
Sample Problem
Only the first one will cancel the units of femtograms to give units of grams.
–15–151 10 g
(2.0 fg) = 2.0 10 g1 fg
–15
–15
1 10 g 1 fg and
1 fg 1 10 g
Essentially, we are multiplying 2.0 fg by 1In order to make the units equal
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Sample Problem, continued
Take the previous answer, and use a similar process to
cancel the units of grams to give units of kilograms.
–15 –183
1 kg(2.0 10 g) = 2.0 10 kg
1 10 g
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Accuracy and Precision
• Accuracy is a description of how close a measurement is to the correct or accepted value of the quantity measured.
• Precision is the degree of exactness of a measurement.
• A numeric measure of confidence in a measurement or result is known as uncertainty. A lower uncertainty indicates greater confidence.
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Accuracy and Precision
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Measurement and Parallax
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Significant Figures
• It is important to record the precision of your measurements so that other people can understand and interpret your results.
• A common convention used in science to indicate precision is known as significant figures.
• Significant figures are those digits in a measurement that are known with certainty plus the first digit that is uncertain.
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Significant Figures
Even though this ruler is marked in only centimeters and half-centimeters, if you estimate, you can use it to report measurements to a precision of a millimeter.
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Rules for Sig Fig
Rule 1
Zeros between other nonzero digits are significant.
Examples
a. 50.3 m has three significant figuresb. 3.0025 s has five significant figures
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Rules for Sig Fig
Rule 2
Zeros in front of nonzero digits are not significant.
Examples
a. 0.892 has three significant figuresb. 0.0008 s has one significant figure
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Rules for Sig Fig
Rule 3
Zeros that are at the end of a number and also to the right of a decimal point are significant.
Examples
a. 57.00 g has four significant figuresb. 2.000 000 kg has seven significant figure
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Rules for Sig Fig
Rule 4
Zeros that are at the end of a number but left of the decimal point are not significant.
Examples
a. 100 m has ONE significant figureb. 20 m has ONE significant figure
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Rules for Sig. Fig.
Extra Rule
Zeros that are at the end of a number but left of the decimal point that are measured to be significant are indeed significant.
Examples
a. A scale measures 1200. kg has four significant figures and is written in scientific notation:
1.200 x 10 kg so Rule 3 applies3
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Rules for Sig Fig
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Rules for Calculating with Significant Figures
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Rules for Rounding in Calculations
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Rules for Rounding in Calculations
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Objectives
• Interpret data in tables and graphs, and recognize equations that summarize data.
• Distinguish between conventions for abbreviating units and quantities.
• Use dimensional analysis to check the validity of equations.
• Perform order-of-magnitude calculations.
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Mathematics and Physics
• Tables, graphs, and equations can make data easier to understand.
• For example, consider an experiment to test Galileo’s hypothesis that all objects fall at the same rate in the absence of air resistance.
– In this experiment, a table-tennis ball and a golf ball are dropped in a vacuum. – The results are recorded as a set of numbers corresponding to the times of the fall and the
distance each ball falls.– A convenient way to organize the data is to form a table, as shown on the next slide.
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Data from Dropped-Ball Experiment
A clear trend can be seen in the data. The more time that passes after each ball is dropped, the farther the ball falls.
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Graph from Dropped-Ball Experiment
One method for analyzing the data is to construct a graph of the distance the balls have fallen versus the elapsed time since they were released.
The shape of the graph provides information about the relationship between time and distance.
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Interpreting Graphs
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Physics Equations• Physicists use equations to describe measured or predicted relationships between physical
quantities.
• Variables and other specific quantities are abbreviated with letters that are boldfaced or italicized.
• Units are abbreviated with regular letters, sometimes called roman letters.
• Two tools for evaluating physics equations are dimensional analysis and order-of-magnitude estimates.
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Equation from Dropped-Ball Experiment
• We can use the following equation to describe the relationship between the variables in the dropped-ball experiment:
(change in position in meters) = 4.9 (time in seconds)2
• With symbols, the word equation above can be written as follows:
y = 4.9(t)2
• The Greek letter (delta) means “change in.” The abbreviation y indicates the vertical change in a ball’s position from its starting point, and t indicates the time elapsed.
• This equation allows you to reproduce the graph and make predictions about the change in position for any time.
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Evaluating Physics Equations