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MeasurementsChapter 2
ConversionsQuantity English unit abb SI unit abb Definition
massPoundsounces
lbsoz gram g
amount of matter in an object
volumeGallonquart
galqt liter L
amount of space an object occupies
lengthInches, feet Yards, miles
in ftyd mi meter m
distance between two objects
time seconds
HrSmin Seconds s finite duration
temperature Fahrenheit ºFKelvinCelsius
K ºC
how hot or cold something is
amount ofsubstance N/A N/A mole mol
the amount of a substance
Based on the Power of 10
King Henry Died By drinking chocolate milkKilo Hecta Deca base deci centi milli
1000 100 10 1 0.1 0.01 0.001
10^3 10^2 10^1 10^0 10^-1 10^-2 10^-3
MEGA 106 M micro 10-6 μ
GIGA 109 G nano 10-9 n
TERA 1012 T pico 10-12 p
Conversion Practice1. 3.68kg = _________g
2. 568cm = _________m
3. 8700mL = _________L
4. 25mg = _________g
5. 0.101cm = ______mm
6. 250mL = _________L
7. 600g = _________kg
8. 8900mm = _______m
9. 0.000004m =
____mm
10. 0.250kg = _______mg
Answers
Accuracy v. Precision Accuracy- How close a measured value
agrees w/ the correct value
Precision-How close ea. Measurement agrees w/ ea. other
Which of the measuring devices
would provide a more accurate measurement?
Why is this one a better device
to use for measuring?
Sec 2-3 Pg 44-57
Sig Figs(a)
1. Exact Numbers: may be counted or defined.
1. Are absolutely accurate2. People in a room.
2. There is some uncertainty in measurements.
3. Sig. Figs. Indicate the uncertainty in the measurements.
1. Digits believed to be correct by those that makes them
2. Can only report ONE estimated digit.
Using Scientific Measurements• Using a calibrated instrument of measure
you can be certain of the accuracy of some of the digits measured.− The last digit of the measurement is
however, always questionable• Excluding the last digit would be misleading
− With the last digit you have some indication of the value’s likely range
• Any measurement reported should consist of the certain digits plus the uncertain digit. − The last digit is uncertain, but it isn’t
insignificant…
Sec 2-3 Pg 44-57
Using Scientific Measurements
• Since only the significant digits are reported it is important to be able to determine all the significant digits in a measurement.− There are a set of rules that allow us to
determine the significance of any figures in any measurement even if we don’t know the origin of the measurement
RULES FOR SIG FIGS1. Zeros (0) used only to position the
decimal are not significant.1. 0.0000593 3 sig figs2. 23000 depends on the measurement
RULES FOR SIG FIGS
2. In x/÷, an answer contains no more sig figs than the least # of sig figs used in the operation.
1. ie: (12.34 cm)*(1.23 cm) = 15.1782 cm2
Correct answer =15.2 cm2
RULES FOR SIG FIGS
1. In +/- the last digit retained in the answer is determined by the position of the first estimated number.
2. In other words
1. (37.24+10.3)=47.5447.52. (27.87-
21.2342)=6.63586.64
Measurements: Sig Figs
Sec 2-3
• Only measurements are given significance.− There are some numbers that aren’t
considered in terms of significance.o Conversion factors have an infinite number
of significant figures (ratios of equal measures, like 1 ft/12 in or 60 sec/1 min)
o Exact numbers also have an infinite number of significant figures, like 20 apples or 10 test tubes
9.0 km
Your Turn…• How many significant figures does each
of the following measurements have?
21000 g 1505 btu 30.0024 sec 21.040 amps 40.000 625 000 kg 6
Pg 44-57
Measurements: Sig Figs
Sec 2-3
• Just because the calculated answer in your calculator has 8 digits in the answer – doesn’t mean they are all significant− Answers calculated from
measurements may not be expressed with more significant digits than any of the original measure- ments
− Calculator answers must be rounded to reflect the least accurate measurement
1. Calculate the area of a crystal surface that measures 1.34 m by 0.7488 m.
2. Calculate how many minutes a project took if the times spent on it each day were 92.5 min, 33.32 min, 25.0 min, 45 min, and 95.33 min.
3. Calculate how many hours the result from #2 would work out to be.
Your Turn…• Carry out each of the mathematical
operation.
1.00 m, 291 min, 4.85 hrs
1. 32,700
Your Turn…• Write the following #’s in sci notation…
3.27 x 104
2. 1,024,0003. 0.004 7100
1.024 x 106
4.7100 x 10-3
Pg 44-57Sec 2-3
2nd function button you push
before the EE button
The EE button is 2nd function of the
comma button
Avoid this button like the plague
4.587E4/1.2E-338225000
Use this button to enter a negative
number
ScientificNotation
On theCalculator█
Derived Units
1. Units that are made up of 2+ basic units, ie. Velocity, force, acceleration.
1. Density1. Amount of mass per unit volume.2. D=m/v3. Unites are g/cm3 or g/mL or g/L4. Cm3 is a unit of volume for solids because v=l*w*h
cm*cm*cm=cm3
2. Example: A 47.23 mL sample of ethanol has a mass of 37.32g. What is its density? (hint: denisty= mass/volume)
Derived Units
Specific Gravity› Ratio of a substance’s density to the
density of H2O
› Density of H2O=1.00g/ml@25 degrees C
› No units
How to: Derived Units
1. Read problems2. Write formula3. Write variables4. Plug in numbers5. Solve
1. For example: Express the density of mercury in lb/ft3 if the density if 13.59 g/cm3.
Your Turn…• A block of Zinc metal has the dimensions
5.0 cm X 7.0 cm X 20.0 cm, and its mass is 5.0 kg. What is the density of the Zinc metal in g/mL? Zinc’s density is 7.13 g/cm3, what is the percent error from the lab?
Dimensional Analysis
Also called the factor label method Easy way to convert between English
and SI (metric). Uses equivalent amounts
› 12 in = 1 ft = 12in/1ft
› 38m=______________ft.
More conversions
English to Metric
Conversions
length
2.54cm=1in39.37in=1m1.609km=1mi
volume1L=1.057qt28.32L=1cubic foot
mass
453.6g=1lb1g=0.03527oz1 metric ton=1.102 standard tonnes
Dimensional Analysis Problems
1. 74cm=__________in2. 25mL=__________tsp3. 50kg=__________lbs4. 160km=__________mi5. 3.6L=__________gal6. 500kg=__________oz7. 100m=__________yds
Dimensional Analysis Answers
1. 29in or 2.9*101in2. 5.1tsp3. 1*102lbs4. 9.94*101mi5. 9.5*10-1gal6. 1.76*104oz7. 1.09*102yds8. Example 2: 8.484*102lbs/ft3
% Error
%Error = (Actual-Theoretical) ___________________ * 100
Theoretical
Will be Θ if the accepted value is greater.
(+) if the accepted value is less.
Problems
Express 12gal in cm3. Suppose Mrs. Fraga’s Bentley contains
a gas tank (handmade) that holds up to 16 gal of fuel. The price of gas is $0.315 per Liter (obviously not a problem). How much would Mrs. Fraga need to charge on her AmEx Platinum for one full tank of gas? Does not include tip.