ch. 3, scientific measurement. measurement : a quantity that has a and a. like 52 meters
TRANSCRIPT
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Ch. 3, Scientific Measurement
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Measurement
• : A quantity that has a and a . Like 52 meters.
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Scientific Notation
• Writing long numbers as smaller ones to a power of ten.
• = 1.4 x 106 = 1.4E6• .00056 = = 5.6E-4• 15,093,000 = 1.5093 x 107 =
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Accuracy vs. Precision• * : How
close a measurement comes to the value.
• * : How close a series of measurements are to .
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Determining Error of a measurement
• = Experimental Value - Accepted Value– Can be positive or
• Percent Error = error / accepted value * 100%– or
– Always • Example, you measured 99 cm, but it is 100 cm.
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• : The digits in a measurement that are known plus one that is not known.– Filled 43.1 mL
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Rules for Sig Figs• Non-Zero Numbers are always significant
– Ex) .236 m has sig figs.• Zeros between non-zero numbers are significant.
– Ex) 7003 m and 40.79 m each have sig figs.• Leftmost zeros are not significant
– Ex) .000099 m, 0.42 m, and .073 m each have sig figs.• Rightmost zeros are significant if they come before or after
a period.– Ex) 9000. m, 90.00 m, and 9.090 m each have sig figs.
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Rules for Sig Figs• Rightmost zeros with no decimal points are no
significant.• Ex) 300 m has sig fig.
• Exactly defined quantities have an number of sig figs.• Seen most when converting between
measurements.• 60 min = 1 hour, 100 cm = 1 m each have an
unlimited number of sig figs.
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Is a Zero a Significant Number or Not?
• 504 L • .06 mL• 50.0 m• 7,000 km
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Sig Figs in Calculations:
• Calculations be more precise than the precise measurement.
• Addition or subtraction - Round the final answer to the same number of decimal places as the measurement with the number of decimal places.– the last “shared column”.
• 13.4 m + 5.254 m = 18.7 m
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Sig Figs in Calculations:
• Multiplication or Division - The final answer should have the number of sig figs as the measurement that has the number of sig figs.
• 2.4526 m x 8.4 m = 21 m
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• In this class, delay rounding until the very end.
• (3.449L + 6.57L) * 8.779L / 5.2L = 17L
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• How much of something you have is given by Units. Like centimeters, kilometers, etc.
• is the standard measurement system for science.
International System of Units
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• * The five SI units used most by chemists are: • Distance = (m) • Mass = kilogram (kg)• Temperature = (K)• Time = second (s)• Volume = liter (L)• Amount = (mol).
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• Prefixes can be used in front of units for powers of 10.
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• = how much “stuff” is in something. How much matter is in something.
• = the pull on something by gravity.
• If I go to the moon, which changes and which stays constant?
- changes, stays the same.
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Temperature:
• Celsius and Kelvin are units of temperature that are the , just shifted.
• K = C + 273• Water freezes at 0 C and at K.• Absolute Zero = 0 K; a K value will never be
negative.
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*Energy
• * - The ability to do work or produce heat.
• (J) is the SI unit of energy.
• (cal) is another unit of energy.
• 1 J = .239 cal
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ConversionsConvert 7 mm to m.
Convert 12.4 Mm to cm.
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• Convert 7 km/ms to m/s
• An experiment asks students to measure 1.50 g of Cu wire. All we have is a 40.0 g spool of Cu. How many students can do the experiment?
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*Density
• * = mass / volume
• What is the density of 2 g of salt in a volume of 4 L?
• What is the density in g/L of 5 kg of salt in a volume of 6 mL?
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If silver has a density of 10.5 g/L, what is the volume of a silver coin that has a mass of 14 g?
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• Density as temperature increases.
• D=m/v• As T increases, V .• Therefore, density decreases.
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Example Problems!!!
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• 1. How many sig figs in: 1.480*105
.00070 1.000080 3.00E3
• 2. Perform these calculations and come up with answers
that have the correct number of sig figs:
5.667 + .34 5.007E3 / 1.20
4.3 - 1.3590 5.309E3 * 3
• 3. Convert 3.4 ng into kg.
• 4. Convert 7E3 cm into Mm.
• 5. What is the mass if a substance with a density of
4.5 g/L has a volume of 3 L?
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6. How many sig figs in: 1010 3000 3000.
3000.0
7. Convert 3 kg into g.
Convert 34 cm into m.
Convert 4 m into cm.
8. You have a 4 kg box. You measure it to be 5.8 kg. What
is the error? The % error?
9. What is the difference between mass and weight?
Accuracy and precision?
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• 11. Put 5,009,000,000 into Scientific Notation
• 12. Put 0.00007890 into Scientific Notation.
• 13. Put 8.7 * 10-4 into a regular number.
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• 14. Which is the largest amount?• A. 2*102 g B. 30 kg C. 45 mg D. 190 g
• 15. Convert 40 Kelvin into Celsius
• 16. Convert 99 Celsius into Kelvin.
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More from Chp 3
• I. Using Measurements
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A. Accuracy vs. Precision
• - how close a measurement is to the accepted value
• - how close a series of measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT
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C. Significant Figures
• Indicate precision of a measurement.
• Recording Sig Figs– Sig figs in a measurement include the _
digits plus a final digit– (See page 24)
2.32 cm
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• 1) How many sig figsafter we estimate?
• 2) Now how many?
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C. Significant Figures
• Counting Sig Figs
– Count all numbers EXCEPT:
• _______________zeros -- 0.0025
• Trailing zeros _________________a decimal point -- 2,500
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4. 0.080
3. 5,280
2. 402
1. 23.50
C. Significant Figures
Counting Sig Fig Examples
1. 23.50
2. 402
3. 5,280
4. 0.080
sig figs
sig figs
sig figs
sig figs
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C. Significant Figures
• Calculating with Sig Figs– Multiply/Divide - The # with the
sig figs determines the # of sig figs in the answer.
(13.91g/cm3)(23.3cm3) = 324.103g
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C. Significant Figures
• Calculating with Sig Figs (con’t)– Add/Subtract - The # with the
decimal value determines the place of the last sig fig in the answer.
3.75 mL
+ 4.1 mL
7.85 mL
3.75 mL
+ 4.1 mL
7.85 mL
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C. Significant Figures
• Calculating with Sig Figs (con’t)– Exact Numbers do not limit the # of sig figs in
the answer.• Counting numbers: 12 students• Exact conversions: 1 m = 100 cm• “1” in any conversion: 1 in = 2.54 cm
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C. Significant Figures
5. (15.30 g) ÷ (6.4 mL)
Practice Problems
= 2.390625 g/mL
6. 18.9 g
- 0.84 g
18.06 g
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D. Scientific Notation
• Converting into Sci. Notation:– Move decimal until there’s digit to its left.
Places moved = .
– Large # (>1) exponentSmall # (<1) exponent
– Only include sig figs.
65,000 kg 6.5 × 104 kg
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D. Scientific Notation
7. 2,400,000 g
8. 0.00256 kg
9. 7 10-5
km
10. 6.2 104
mm
Practice Problems
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D. Scientific Notation
• Calculating with Sci. Notation (5.44 x 107 g) / (8.1 x 104 mol) =
Type of your calculator:
5.44 EE 7 / 8.1 EE 4 =
671.6049383
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E. SI Units
Quantity Base Unit Abbrev.
Length
Mass
Time
Temp
meter
kilogram
second
kelvin
s
K
Amount mole
Symbol
l
m
t
n
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E. SI Units
mega- M 106
deci- d 10-1
centi- c 10-2
milli- m 10-3
Prefix Symbol Factor
micro- 10-6
nano- n 10-9
pico- p 10-12
kilo- k 103
BASE UNIT --- 100
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F. Derived Units
• Combination of base units.
• (m3 or cm3) – length length length
D = MV
1 cm3 = 1 mL1 dm3 = 1 L
(kg/m3 or g/cm3)mass per volume
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Problem-Solving Steps
1. _
2. Plan
3. Compute
4. _
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Density
• An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.
GIVEN:
V = D =
M = ?
WORK:
M = M =
M =
V
MD
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Density
• A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?
GIVEN:
D =
V = ?
M =
WORK:
V =
V =
V =V
MD
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SI Prefix Conversions
mega- M 106
deci- d 10-1
centi- c 10-2
milli- m 10-3
Prefix Symbol Factor
micro- 10-6
nano- n 10-9
pico- p 10-12
kilo- k 103
mo
ve le
ft
mo
ve r
igh
t BASE UNIT --- 100
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SI Unit Conversions
• King __doofus can milk many newts.
• k__ d c m m n
• kilo, deci, , milli, ,
• What’s yours?
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=
SI Prefix Conversions
NUMBERUNIT
NUMBER
UNIT
532 m = _______ km
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SI Prefix Conversions
1) 20 cm = ______________ m
2) 0.032 L = ______________ mL
3) 45 m = ____ mm
4) 805 dm = ______________ km
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Dimensional Analysis
• Steps:
1. Identify starting & units.
2. Line up conversion factors so units .
3. Multiply all numbers & divide by each bottom number.
4. Check units & answer.
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Dimensional Analysis
• Lining up conversion factors:
1 in = 2.54 cm
2.54 cm 2.54 cm
1 in = 2.54 cm
1 in 1 in
= 1
1 =
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Dimensional Analysis
• How many milliliters are in 1.00 quart of milk? (1L = 1.057 qt)
1.00 qt
qt mL
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Dimensional Analysis
• You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. (1 kg = 2.2 lbs)
lb cm3
1.5 lb
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Dimensional Analysis
5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? (1 in=2.54cm)
8.0 cm
cm in