How many mm in a meter?How many mm in a meter?How may kg in a g?How may kg in a g?What is the deal with kilogram anyway?What is the deal with kilogram anyway?Are mm and Mm the same?Are mm and Mm the same?Are m and M the same?Are m and M the same?

What is the correct symbol?What is the correct symbol?

1.1. MilliMilli

2.2. MicroMicro

3.3. MegaMega

4.4. NanoNano

5.5. CentiCenti

6.6. KiloKilo

8/298/29

Pick up graph paper , lab, ruler, calculator Pick up graph paper , lab, ruler, calculator and colored penciland colored pencil

Yesterday we went over OOO and Isolating Yesterday we went over OOO and Isolating variables. Math Inventory was checked variables. Math Inventory was checked for HW.for HW.

Quiz delayed until next Wed.Quiz delayed until next Wed.

8/308/30You will have 10 minutes to finish your You will have 10 minutes to finish your

graphing lab. When completed staple graphing lab. When completed staple graph, post lab questions, and data table graph, post lab questions, and data table together in that order. Make sure each together in that order. Make sure each page has your first & last name and period. page has your first & last name and period. Place in blue sorter.Place in blue sorter.

Reading Quiz delayed until next Wed. We will Reading Quiz delayed until next Wed. We will also have a quiz on Friday over Trig and also have a quiz on Friday over Trig and dimensional analysisdimensional analysis

II. Measurement and Problem

Solving

Why Measure?

2 Categories of measurement

Measurements Qualitative measurements - adjectives Quantitative measurements – involve

actual numbers (quantities) These depend on reliability of the

measuring instrument. These depend on care with which it is

read.

What type of measurement is more useful?

What two items must one always include What two items must one always include when taking a measurement?when taking a measurement?

Numerical PortionNumerical Portion

UnitUnit

Measurements REQUIRE Units of Measure

The standards of measurement used in science are those of the metric system.

The metric system is also known as the International System of Units (SI), established in 1960.

This system’s focus is simplicity and is based on 10 or multiples of 10.

There are 7 base units.

What are the seven base measurements?

What are the si base units for:What are the si base units for:

1.1. LengthLength

2.2. MassMass

3.3. TimeTime

4.4. Luminous IntensityLuminous Intensity

5.5. Amount of a substanceAmount of a substance

6.6. TemperatureTemperature

7.7. Electric CurrentElectric Current

7 SI Base Units7 SI Base Units(all other units derived from a combination of these)(all other units derived from a combination of these)

Base QuantityBase Quantity Base UnitBase Unit SymboSymboll

LengthLength MeterMeter mm

MassMass KilogramKilogram kgkg

TimeTime SecondSecond ss

TemperatureTemperature KelvinKelvin KK

Amount of a substanceAmount of a substance MoleMole molmol

Electric CurrentElectric Current AmpereAmpere AA

Luminous IntensityLuminous Intensity CandelaCandela cdcd

Why is volume not listed as a base unit?Why is volume not listed as a base unit?

Measurements REQUIRE Units of Measure

Sometimes, non-SI units are used.Liter, Celsius, calorie

Others are derived units made by joining other units.Speed (miles/hour)Density (grams/mL)

Making and recording measurements

Significant Figures: Rules

Significant Figures

Significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.

Significant FiguresSignificant figures result from directly

measuring an object. It shows the precision of the measurement.

Again, the precision of the measurement depends upon the type of measuring instrument.

Use a PRIORITIZED set of rules to determine the number of SF in a calculation.

Rule 1 All nonzero digits are significant.

a. 234

b. 1678

c. 0.23

a. 234

b. 1678

c. 0.23

Rule 2 All zeros between nonzero digits

are significant.

Example

a. 202

b. 1003

c. 0.200105

Example

a. 202

b. 1003

c. 0.200105

Rule 3 Zeros to the right of a nonzero digit

but to the left of the decimal are NOT significant unless otherwise

indicated.

Example

a. 200

b. 109,000

Example

a. 200

b. 109,000

Rule 4All zeros to the right of a decimal point but to the left of a nonzero

digit are NOT significant.

Example

a. 0.0032

b. 0.01294

c. 0.00000002

Example

a. 0.0032

b. 0.01294

c. 0.00000002

Rule 5All zeros to the right of a decimal

point and following a nonzero digit are significant.

Example

a. 20.00

b. 0.07080

Example

a. 20.00

b. 0.07080

Ex A: How many Significant Figures?10001000100010001000.01000.00

In physics we ask you to record all answers to 3 significant figures. What is an easy way to do this?

Scientific Notation Coefficient raised to power of 10 Specific format: number between 1

and 10

Why are Scientific Notation and Significant Figures important?Have examples here of SN problems

8/26 It’s Friday, It’s Friday!

Get a calculatorHave Measurement notes outTurn in cylinder lab to blue sorter. Make sure you

have your first & last name, as well as period.Make sure graph is attached.Quiz over reading on MondayGoal:

Calculating accuracy & precisionReviewing Metrics and Dimensional Analysis

Skip next two slides

Round the answer of a calculation to the same number of significant figures as the least number of significant figures in the set of recorded measurements.

(100)(0.575) = 57.5(100)(0.575) = 60

SF: Multiplication and Division

Multiplication and Division Using Significant Figures

Examples

2.40 cm x 3 cm (fewest # of SF is 1)

2.40 cm x 3 cm = (7.2 cm2) = 7 cm2

0.50 cm2 ÷ 0.0038 cm (fewest # of SF is 2)

0.50 cm2 ÷ 0.0038 cm = (131.5 cm2) = 130 cm

12000 g ÷ 1.5045 mL (fewest # of SF is 2)

12000 g ÷ 1.5045 mL = (7976 g/mL) = 8000 g/mL

9/3 I hope you had a great weekend. You need a calculator everyday until next yearFriday you turned in Cardboard Mass Lab.

If you have not done so, turn into red basket. We also discussed measurement and Sig Figs. Have Example B on Measurement notes out and be ready to go over.

Pick up 02 Meas WS I. Complete the sig fig problems at the top now.

Your HW is any of the 5 DA problems 1-6

Determine how many SF are in examples A-F

A.59.300 joules

B.0.00384 in

C.4.84 x 103 m

D.3003 N

E.202,000 cm

F.4060 mm

A.59.300 joules

B.0.00384 in

C.4.84 x 103 m

D.3003 N

E.202,000 cm

F.4060 mm

Accuracy vs. PrecisionAccuracy refers to the closeness of a value to the

true value.Precision is the repeatability of a result. It is an

indicator of the scattering in the data. (describes range)Assume we measure the weight of a computer

monitor and obtain values of 3.001 N, 3.000 N, 2.999 N, and 3.000 N. These numbers are precise enough for us to believe that if we measure in again we would obtain 3.000 ± 0.001 N.

Precision also refers to the exactness of a measurementThe smaller the unit of measure, the more

preciseWhich is more precise?1.5m or 1.571m4.2 km or 4.2 mm

Error

SystematicAffect each measurement the sameExamples?Calibration, ignoring a variable RandomDo not affect each measurement the sameExamples?ParallaxHumanExamples?Recording in wrong scale

Uncertainty in Measurements Accepted value – correct value

based on reliable references AKA Actual Value

Experimental value – the value measured in the lab AKA Observed Value

Error = Absolute Error Error = Experimental – Actual

% Error = Relative Error %Error = | absolute error | x 100%

actual

The goal:

Be accurate and precise

Ex C: A chemical reaction…

What is the absolute error?

What is the % error?

Ex C: A chemical reaction…

What is the absolute error?

4.15

What is the % error?

27.9%

Ex. D: Consider the following sets of data. The accepted measurement is 6.8.Data Set I 5.8 9.3 5.7 4.8

Data Set II 5.3 5.4 5.6 5.3

Data Set III9 8 6 6

Which data set is the most accurate? How would you determine this?Which data set is the most precise? How would you determine this?

Consider the following sets of data. The accepted measurement is 6.8.

Data Set I 5.8 9.3 5.7 4.8Ave 6.4 Range 4.5

Data Set II 5.3 5.4 5.6 5.3Ave 5.4 Range 0.3

Data Set III9 8 6 6Ave 7.25 Range 3

Which data set is the most accurate? I

Which data set is the most precise? II

Ex E: Which measurement is the most precise?

2525.425.4125.41325.413830

9/4 Place Triangle Problems (mathref04) in blue sorter.Continue working on measurement lab

when you come in. Design your graph, but do not draw the line until I have a chance to speak to the class.

If you were absent yesterday, see me about scheduling quiz makeup.

You may work on lab until last 20 minutes of class.

Graphing: What is line of best fit mean? How do you do it?y = mx + bRemember m is the slope and b

represents the y interceptIf y intercept is 0, the y=mxRearranged, m = ?m= y2-y1/x2-x1

DO NOT FORGET UNITS!!!!!Interpolate vs Extrapolate?

Metric Mania:Using metric makes math easy! How many grams do I have if I have 1 How many grams do I have if I have 1

yottagram? (1Yg) yottagram? (1Yg) FYI the earth has a mass of 5983YgFYI the earth has a mass of 5983YgWhat’s bigger a terabyte or a picobyteWhat’s bigger a terabyte or a picobyte

Ex F: Prefixes Fill in chart beside this Ex F: Prefixes Fill in chart beside this diagramdiagram

KHD___dcm

GXXMXXKHD___dcmXXμXXn

Check your work

10 is 101 is ten10-1 is tenth102 is hundred10-2 is hundredth103 is thousand10-3 is thousandth

CHECK your work!

106 is million10-6 is millionth109 is billion10-9 is billionth1012 is trillion10-12 is trillionth

What do the following prefixes mean?What do the following prefixes mean?

1.1. CentiCenti

2.2. GigaGiga

3.3. DeciDeci

4.4. KiloKilo

5.5. nanonano

How many minutes in a year?How many minutes in a year?

DimensionalDimensional AnalysisAnalysis

Used to convert between Used to convert between different units of measurementdifferent units of measurement

This is done by multiplying by This is done by multiplying by factors of 1factors of 1

Converting up on down the metric system Converting up on down the metric system using dimensional analysisusing dimensional analysis

What do you have?What do you have?What do you want?What do you want?Is your answer going to be larger or Is your answer going to be larger or

smaller than the starting number?smaller than the starting number?What do you know?What do you know?Remember you must be able to cancel out Remember you must be able to cancel out

all units except the one you want to end up all units except the one you want to end up withwith

Step 1Step 1Write down the number and unit Write down the number and unit

that you are starting withthat you are starting with

Step 2Step 2Find out how to arrive at your Find out how to arrive at your

final unit by using known final unit by using known conversion factorsconversion factors

Step 3Step 3Set up your conversion factor so Set up your conversion factor so

that the units cancelthat the units cancel

ExampleExampleConvert 5 m into km:Convert 5 m into km:

Step 1: you start with 5 m

Step 2: you need to get to kmStep 3: you know that: 1km = 1000 m

Step 4: 5 m X 1km = 1000 m

0.005m

**Always multiply every number across the top ,then multiply every number across the bottom. Finally divide the product of the top by the product of the bottom. Record number and unit.

Ex G: Convert 170 cm to km.

170 cm1

Convert 170 cm to km.

170 cm m km1 cm m

Convert 170 cm to km.

170 cm 1 m 1 km1 100 cm 1000 m

Convert 170 cm to km.

170 cm 1 m 1 km1 100 cm 1000 m

0.0017 km or 1.7 × 10-3 km

Wed 9/1 You will need a calculator and some paperGoals: Apply logic to problem solving.

Use dimensional analysis correctly!!!!!Due: 02MeasWSI a-o Hold on to this.Complete the chart on page four. You

may want to write the prefix beside the value.

Ex: 10 is 101 ten dekaEx: 10 is 10-1 tenth deci

Ex H: Convert 83.96 mg to μg.

83.96 mg1

Convert 83.96 mg to μg.

83.96 mg g μg1 mg g

Convert 83.96 mg to μg.

83.96 mg 1 g 1 × 106 μg1 1000 mg 1 g

8.396 × 104 μg

Ex I: Convert 87 feet to meters.

87 feet1

Convert 87 feet to meters.

87 feet mile km m1 feet mile km

Convert 87 feet to meters.

87 feet 1 mile 1 km 1000 m1 5280 feet 0.621 mile 1 km

27 m

Ex J: Convert 14.8 pounds to cg.

14.8 #1

Convert 14.8 pounds to cg.

14.8 # g cg1 # g

Convert 14.8 pounds to cg.

14.8 # 454 g 100 cg1 1 # 1 g

6.72 × 105 cg

Ex K: Convert 55 mi/hr to in/s.

55 mihr

Convert 55 mi/hr to in/s.

55 mi ft in hrhr mi ft s

Convert 55 mi/hr to in/s.

55 mi 5280 ft 12 in 1 hrhr 1 mi 1 ft 3600 s

970 in/s

Ex L- N on your own

What is the volume in L of 14 pounds of Al?

Which is larger?

A. 1 millimeter

B. 1 centimeter

A flash drive has 8 Gigabytes. How many bytes does this equal?

A. 8000

B. 8,000,000

C. 8,000,000,000

If you swam fly at a consistent speed which pool would you have a better time in 25 yards or 25 meters?

A. meters

B. yards

What’s bigger an inch or a centimeter?

A. inch

B. centimeter

What units would be used to measure What units would be used to measure the distance from here to Dallas?the distance from here to Dallas?

A. cm

B. mm

C. km

D. m

cm, mm, km or mcm, mm, km or m

Copy the following

10 is 101 is ten10-1 is tenth102 is hundred10-2 is hundredth103 is thousand10-3 is thousandth

Complete the following

106 is _____________10-6 is _____________109 is _____________10-9 is _____________1012 is _____________10-12 is _____________

Copy and Finish

Kilo k 103

Mega M 106

Giga ___ ____Tera ___ ____

Check your work

Kilo k 103

Mega M 106

Giga G 109

Tera T 1012

Copy and finish the list

centi c 10-2

milli m 10-3

micro ____10 ____

nano ____10 ____

pico ____10 ____

CHECK your work!

centi c 10-2

milli m 10-3

micro 10-6

nano n 10-9

pico p 10-12

Copy and Finish the List

1 cm = 10-2 m 1 m = 102 cm1 mm = 10-3 m 1 m = 103 mm1 m = ______ 1 m = ______1 nm = ______ 1 m = ______1 pm = ______ 1 m = ______

CHECK your work!

1 cm = 10-2 m 1 m = 102 cm1 mm = 10-3 m 1 m = 103 mm1 m = 10-6 m 1 m = 106 m1 nm = 10-9 m 1 m = 109 nm1 pm = 10-12 m 1 m = 1012 pm

9/5 Diameter vs Circumference LabCollect DataPerform Regression Analysis using diameter as

Independent variable or X (list 1) and circumference as Dependent Variable or Y (list 2)

Sketch resulting Graph (step 24)Record Formula (step 31)Sketch final graphUsing Formula from step 31 determine the

circumference of an object with a diameter of 6.19 cm.

9/5 FRIDAY!!!!!!!!Remember we have a test on MondayHow many cm in a decimeter?What is the formula for density?Write 38,372 with 3 significant figures

428,600,00 is Sci. Not. to two sig figs.0045 in Sci.NotWhat is the difference between an accepted

measurement and an experimental measurement?What is the difference between a quantitative and

qualitative measurement?

SKIP Copy and Finish Consider for HW100 cm > 100 nm200 nm ________ 25 m

6x10-6 mm ________ 5x103 pm

1280 nm _____ 1.28x10-3 mm

700 nm ________ 1.0 m

SKIP Copy and Finish

100 cm > 100 nm200 nm < 25 m

6x10-6 mm > 5x103 pm

1280 nm = 1.28x10-3 mm

700 nm < 1.0 m

SKIP Copy and Finish

1 cm = 104 m1 m = 10-4 cm1 mm = 109 pm 1 pm = 10-9 mm1 m = ___mm 1 mm = ___ m1 nm = ___ cm 1 cm = ___ nm1 pm = ___ m 1 m = ___ pm

SKIP Copy and Finish

1 cm = 104 m1 m = 10-4 cm1 mm = 109 pm 1 pm = 10-9 mm1 m = 10-3 mm 1 mm = 103 m1 nm = 10-7 cm 1 cm = 107 nm1 pm = 10-6 m 1 m = 106 pm

SKIP Copy and Finish

1 km = 103 m 1 m = 10-3 km1 Mm = 106 m 1 m = 10-6 Mm1 Gm = _____ 1 m = ______1 Tm = _____ 1 m = ______

SKIP Copy and Finish

1 km = 103 m 1 m = 10-3 km1 Mm = 106 m 1 m = 10-6 Mm1 Gm = 109 m 1 m = 10-9 Gm1 Tm = 1012 m 1 m = 10-12 Tm

SKIP Copy and Finish

100 km > 10 000 m200 Mm ___ 25 Gm5 x 10-6 Tm ____ 6 x 103 km1280 km ___ 1.28 x 10-3 Gm700 000 m ___ 1.0 Mm

SKIP Copy and Finish

100 km > 10 000 m200 Mm ? 25 Gm5 x 10-6 Tm < 6 x 103 km1280 km < 1.28 x 10-3 Gm700 000 m < 1.0 Mm

SKIP Copy and Finish

1 Mm = 10-6 Tm 1 Tm = 106 Mm1 Gm = 106 km 1 km = 10-6 Gm1 Tm = ___ Gm 1 Gm = ___ Tm1 km = ___ Mm 1 Mm = ___ km

SKIP Copy and finish converting to m’s

350 km = 350 x 103 m = 3.5 x 105 m8x10-4 Gm = 8x10-4 x109 m = 8x105 m0.06 Mm = 3 x 10-8 m =45 cm = 650 nm = 7 x 105 cm =

Lemmings

Lemming runs off 35 m cliff at 22 m/s. Where does it land?

Lemming lands 17 m out from the base of a 5. 3 m cliff. How fast was it going?

The answer cannot be more specific than the least specific number in the problem set.

SF:Addition and Subtraction

Which is the least specific measurement of the following?

1300.8752006795.3386.0

Add these numbers togetherAnswer should be record only in

the100 placeThe answer is600

Addition and Subtraction Using Significant Figures

Examples

2.40 cm + 3 cm (least specific value records to the ones place)

2.40 cm + 3 cm = 5.40 cm = 5 cm

0.50 m - 0.0038 m (least specific value records to the tenths place)

0.50 m - 0.0038 m = (0.4962 m) = 0.50 m