significant figures density % error. significant figures the number of digits reported in a...
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Significant FiguresDensity% Error
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Significant Figures
The number of digits reported in a measurement.
All the known digits plus one estimated value.
The number of significant figures possible depends upon the piece of equipment used to take the measurement.
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Significant Figures
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Rules for Significant Figures1. Non-zero numbers are always significant.2. Zeros between non-zeros are always
significant.3. All final zeros to the right of the decimal
place are significant. 4. Zeros that act as placeholders are NOT
significant. 5. Counting numbers and defined constants
have an infinite number of significant figures.
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Practicing Significant FiguresDetermine the number of sig figs in the following numbers.
1)0.02
2)70001
3)5600
4)4.100
5)3.1416
(π)
6)2.80 x
105
0.02
70001
5600
4.100
3.1416 (π)
2.80 x 105
1
5
2
4
Infinite
3
Red numbers=significant Black numbers=not significant
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Rules for Rounding
If the digit to the immediate right of the last sig fig is 5-9, round up.
If not, leave as is.
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Significant Figures and Calculators
When using a calculator, you should do the calculation using the digits allowed by the calculator and round off only at
the end of the problem.
Do not round off in the middle of the problem!
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Sig Figs and Addition/Subtraction
+ - + - + - + - + - + - + - +When you add or subtract, you answer must have the same number of digits to
the right of the decimal point as the original value with the fewest digits to
the right of the decimal place.+ - + - + - + - + - + - + - +
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Sig Figs and Multiplication/Division
When you multiply or divide, your answer must have the same number of significant figures as the original value
with the least significant figures.
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Practicing Significant Figures
3.33 m2
25 m
53 mL
26.6 g
6.7 cm3
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Density
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Which weighs more, a pound of bricks or a pound of feathers?
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Density
When something feels heavy, you are noting its density.
Density—the mass of an object per unit volume
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Density
D= The unit for density should always
be some unit for mass over some unit for volume.
Usually it is g/mL, g/L or kg/m3
mv
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Practice Problem #1
What is the density of an object that has a mass of 22.5g and a
volume of 30.4 mL?
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Practice Problem #2
If a cube has sides that are 8.2 mL each and a total mass of 46.1g,
what is its density?
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Practice Problem #3
What is the volume of isopropyl alcohol if its mass is 45.22g and it
has a density of 0.899 g/mL?
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Percent Error
A way to evaluate the accuracy of data.
Percent Error=Ratio of the error to the accepted value
│Accepted value – Measured value │Accepted value X 100%
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Percent Error
If your measurement of a liquid is 123.4 mL but the actual amount is 125.0 mL, what is the percent error of the
measurement?
125.0 mL – 123.4 mL 1.6 mL________________________________________ _______________
125.0 mL 125.0 mL = X 100% = 1.3%