measurements. number vs. quantity a number without a unit is meaningless a number without a unit is...
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MeasurementsMeasurements
Number vs. QuantityNumber vs. Quantity A number without a unit is A number without a unit is
meaninglessmeaningless It is 4 longIt is 4 long 4 what?4 what? Scientists use the Scientists use the metric systemmetric system or or SISI
for for le System Internationale d’Unitsle System Internationale d’Units Makes sharing data across countries Makes sharing data across countries
easiereasier
Number vs. QuantityNumber vs. Quantity Quantity has aQuantity has a number + unit number + unit
UNITS MATTER!!UNITS MATTER!!
SI “Base” UnitsSI “Base” UnitsQuantity Unit Abbreviatio
nLength meter m
Mass gram g
Temperature
kelvin K
Electric current
ampere A
Amount of substance
mole mol
Luminous intensity candela
cd
Measuring lengthMeasuring length
Use a rulerUse a ruler Line up from zero not the end of the rulerLine up from zero not the end of the ruler Numbered divisions are Numbered divisions are centimeterscentimeters Small divisions are Small divisions are millimetersmillimeters There are 10 millimeters in 1 centimeterThere are 10 millimeters in 1 centimeter
0 1 2 3 4
VolumeVolume VolumeVolume – the amount of space – the amount of space
occupied by an objectoccupied by an object
Volume (cmVolume (cm33)= length x width x height)= length x width x height LiterLiter (L) is also a common unit (for (L) is also a common unit (for
liquids)liquids)
1 L = 1 quart; about 1/4 of a gallon 1 L = 1 quart; about 1/4 of a gallon
1 mL is about 20 drops of water or 1 1 mL is about 20 drops of water or 1 sugar cube, 1 mL = 1 cmsugar cube, 1 mL = 1 cm33
Measuring VolumeMeasuring Volume Use a Use a graduated cylindergraduated cylinder..
The water will curve in the The water will curve in the cylinder (cylinder (meniscus).meniscus).
Hold it level with your eye.Hold it level with your eye.
Read the Read the bottombottom of the of the meniscus.meniscus.
Measures in Measures in milliliters mLmilliliters mL..
10
20
30
Used to measure Used to measure volume of an volume of an irregular solid.irregular solid.
1.1. Fill water to spout.Fill water to spout.
2.2. Put object in.Put object in.
3.3. Catch water that Catch water that comes out.comes out.
4.4. Find volume of that Find volume of that water.water.
Water DispWater Displacement Tanklacement Tank
MassMass WeightWeight is the is the forceforce of gravity on an of gravity on an
object; object; MassMass is the is the amountamount of matter. of matter. 1 1 gramgram is defined as the mass of 1 is defined as the mass of 1
cmcm33 of water at 4 ºC. of water at 4 ºC. 1 g = 1 paper clip1 g = 1 paper clip 1 kg = 1 L of water1 kg = 1 L of water 1 kg = 2.5 lbs1 kg = 2.5 lbs 1 mg = 10 grains of salt or 2 drops of 1 mg = 10 grains of salt or 2 drops of
water.water.
Measuring MassMeasuring Mass Use a triple beam balanceUse a triple beam balance First balance it at zero.First balance it at zero. Then put item onThen put item on Then move one weight at a timeThen move one weight at a time When balanced, add up the When balanced, add up the
weightsweights
0 1 2 3 4 5 6 7 8 9 10
0 10 20 30 40 50 60 70 80 90 1000 10 20 30 40 50 60 70 80 90 100
0 100 200 300 400 500
Triple beam Balance
Accuracy and PrecisionAccuracy and Precision
AccuracyAccuracy - the - the closenesscloseness of a of a measurement to the measurement to the accepted valueaccepted value. .
PrecisionPrecision – the – the closenesscloseness of a of a setset of of measurements of the same quantity, measurements of the same quantity, made the same way. made the same way.
AccuracyAccuracy AccuracyAccuracy - the closeness of a measurement - the closeness of a measurement
to the to the accepted valueaccepted value.. Ex.Ex. 10 pennies have a mass of exactly 30 g; that 10 pennies have a mass of exactly 30 g; that
is the is the accepted valueaccepted value.. Jan found the mass of 10 pennies; she got 29.8 g.Jan found the mass of 10 pennies; she got 29.8 g. Tom found the mass of 10 pennies; he got 28.6 g.Tom found the mass of 10 pennies; he got 28.6 g. Jan’s measurement is Jan’s measurement is more accuratemore accurate than Tom’s than Tom’s
because her 29.8 gbecause her 29.8 g
is is closercloser to 30 g to 30 g
than Tom’s 28.6 g. than Tom’s 28.6 g.
PrecisionPrecision PrecisionPrecision – – closeness of a closeness of a setset of measurements of measurements
of the same quantity, made the same way.of the same quantity, made the same way. Ex. 10 pennies have a mass of 30 g; that is the Ex. 10 pennies have a mass of 30 g; that is the
accepted valueaccepted value.. Jan measured the mass of 10 pennies 4 times. Jan measured the mass of 10 pennies 4 times.
She got the following She got the following setset of measurements: of measurements: 32.3 g, 32.2 g, 32.3 g, 32.3 g, 32.2 g, 32.3 g,
32.4 g32.4 g
These measurements are NOT These measurements are NOT accurate, but these measurements accurate, but these measurements
are are preciseprecise because because they are close they are close to each otherto each other..
OutliersOutliers – – data points that don’t fit the trend.data points that don’t fit the trend.That point is likely the result of an error.That point is likely the result of an error.
Derived UnitsDerived Units
Combination of base units.Combination of base units. VolumeVolume - length - length width width height height
1 cm1 cm33 = 1 mL 1 dm = 1 mL 1 dm33 = 1 L = 1 L DensityDensity - mass per unit volume - mass per unit volume
(g/cm(g/cm33))
D = MV D
M
V
Density Problem exampleDensity Problem example An object has a volume of 825 cmAn object has a volume of 825 cm33
and a density of 13.6 g/cmand a density of 13.6 g/cm33. Find its . Find its mass.mass.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
M = ?
WORK:
M = DV
M = (13.6 g/cm3)(825cm3)
M = 11,220 g
DM
V
Density Problem 1Density Problem 1
1) A liquid has a density of 0.87 g/mL. 1) A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of What volume is occupied by 25 g of the liquid?the liquid?
GIVEN:
D = 0.87 g/mL
V = ?
M = 25 g
DM
V
WORK:
V = M D
V = 25 g
0.87 g/mL
V = 28.7 mL
Density Problem 2Density Problem 22) You have a sample with a mass of 2) You have a sample with a mass of
620 g & a volume of 753 cm620 g & a volume of 753 cm33. Find . Find density.density.
GIVEN:
M = 620 g
V = 753 cm3
D = ?
DM
V
WORK:
D = M V
D = 620 g
753 cm3
D = 0.82 g/cm3
Metric SystemMetric System
Measurements have two partsMeasurements have two parts Base unit and prefixBase unit and prefix Prefixes multiply or divide the Prefixes multiply or divide the
base units by multiples 10base units by multiples 10 Prefixes are the same for all unitsPrefixes are the same for all units
SI Unit PrefixesSI Unit Prefixes
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
SI Prefix ConversionsSI 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 d
ecim
al le
ft
mo
ve d
ecim
al r
igh
t
Prefix ConversionsPrefix Conversions10-3 Mili
m
1 Unit
10-2 Centi
c
10-1 Deci
d
101 deka
dk
102 hecta
h
103
kilo
k
King Henry danced merrily down central main.
King Henry died Monday drinking chocolate milk.Move the decimal in the direction & Move the decimal in the direction & number of spaces as indicated in the number of spaces as indicated in the above chart.above chart.
Metric Conversion SummaryMetric Conversion Summary
To go from a large unit to a smaller To go from a large unit to a smaller unit:unit:
MOVE THE DECIMAL TO THE MOVE THE DECIMAL TO THE RIGHTRIGHT
To go from a small unit to a larger To go from a small unit to a larger unit:unit:
MOVE THE DECIMAL TO THE MOVE THE DECIMAL TO THE LEFTLEFT
SI Prefix ConversionsSI Prefix Conversions
1. Find the difference between the 1. Find the difference between the
exponents of the two prefixes.exponents of the two prefixes.
2. Move the decimal that many places.2. Move the decimal that many places.
To the leftor right?
=
SI Prefix ConversionsSI Prefix Conversions
NUMBERUNIT
NUMBER
UNIT
532 m = _______ km0.532
Metric conversionsMetric conversions
A common race is the 5 K, which is 5 A common race is the 5 K, which is 5 km. How many meters is this?km. How many meters is this?
Unit given -kmUnit given -km Unit wanted –mUnit wanted –m The unit gets smaller, so the number The unit gets smaller, so the number
must get biggermust get bigger 1000 m = 1 km1000 m = 1 km
Conversion ProblemsConversion Problems1) 20 cm = 1) 20 cm = ______________ m______________ m
2) 0.032 A = 2) 0.032 A = ______________ mA______________ mA
3) 45 3) 45 m = m = ______________ nm______________ nm
4) 805 dm = 4) 805 dm = ______________ km______________ km
0.2
0.0805
45,000
32
3
3
cm
gcm
Dimensional AnalysisDimensional Analysis
The “Factor-Label” MethodThe “Factor-Label” Method Units, or “labels” are canceled, Units, or “labels” are canceled,
or “factored” outor “factored” out
g
Dimensional AnalysisDimensional Analysis
Steps:Steps:
1. Identify starting & ending units.1. Identify starting & ending units.
2. Line up conversion factors so units 2. Line up conversion factors so units cancel.cancel.
3. Multiply all top numbers & divide by 3. Multiply all top numbers & divide by each bottom number.each bottom number.
4. Check units & answer.4. Check units & answer.
Dimensional Analysis ProblemDimensional Analysis Problem
Lining up conversion factors: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 =
1 in = 2.54 cm
Dimensional AnalysisDimensional Analysis
Your European hairdresser wants to Your European hairdresser wants to cut your hair 8 cm shorter. How cut your hair 8 cm shorter. How many inches will he be cutting off?many inches will he be cutting off?
8 cm8 cm 1 in1 in
2.54 2.54 cmcm
= 3.15 = 3.15 inin
cm in
Dimensional AnalysisDimensional Analysis
How many milliliters are in 1 How many milliliters are in 1 quart of milk?quart of milk?
1 qt1 qt 1 L1 L
1.057 qt1.057 qt= 946 mL= 946 mL
qt mL
1000 1000 mLmL
1 L1 L
Dimensional AnalysisDimensional Analysis5) Assume your mass is 55 kg. 5) Assume your mass is 55 kg.
How many pounds do you weigh?How many pounds do you weigh?
55 55 kgkg
2.2 lb2.2 lb
1 kg1 kg= 121 = 121
lblb
kg lb
Dimensional AnalysisDimensional Analysis6) How many feet long is a 5K (5 6) How many feet long is a 5K (5
km) race?km) race?
5 km5 km 1 mi1 mi
1.609 1.609 kmkm
= 16,408 = 16,408 ftft
km ft
5280 ft5280 ft
1 mi1 mi
Dimensional AnalysisDimensional Analysis
7) How many grams does a 10-lb. 7) How many grams does a 10-lb. bag of potatoes weigh?bag of potatoes weigh?
10 lb10 lb 1 kg1 kg
2.2. lb2.2. lb= 4545 g= 4545 g
lb g
1000 g1000 g
1 kg1 kg
Dimensional AnalysisDimensional Analysis8) Taylor football needs 550 cm for a 8) Taylor football needs 550 cm for a
1st down. How many yards is this?1st down. How many yards is this?
550 550 cmcm
1 in1 in
2.54 2.54 cmcm
= 6.01 = 6.01 ydyd
cm yd
1 ft1 ft
12 12 inin
1 1 yydd
3 ft3 ft
Types of GraphsTypes of Graphs Line GraphLine Graph
shows the shows the relationship relationship between 2 between 2 variablesvariables
Dep
end
ent
Var
iab
le
Independent Variable
Types of GraphsTypes of Graphs Bar GraphBar Graph
shows shows information information collected by collected by countingcounting
Types of GraphsTypes of Graphs
Pie GraphPie Graph shows shows
distribution of distribution of parts within a parts within a whole whole quantityquantity
Graphing & DensityGraphing & DensityM
ass
(g)
Volume (cm3)
Δx
Δyslope D
V
M