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Page 1: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Chapter 2“Scientific

Measurement”

Page 2: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

• OBJECTIVES:

- Determine the fundamental units of SI

- Convert measurements to various units and scientific notation.

- Distinguish accuracy and precision and relate it to significant figures

- Determine the number of significant figures in measurement and the rules of rounding off

Page 3: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Types of Observations and Types of Observations and MeasurementsMeasurements

• We makeWe make QUALITATIVEQUALITATIVE observations of reactions — observations of reactions — changes in color and physical changes in color and physical state.state.

• We also makeWe also make QUANTITATIVE QUANTITATIVE MEASUREMENTSMEASUREMENTS, which involve , which involve numbersnumbers..

–UseUse SI unitsSI units — based on the — based on the metric systemmetric system

Page 4: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Stating a MeasurementStating a Measurement

In every measurement there is aIn every measurement there is a

Number Number followed by a followed by a

Unit Unit from a measuring devicefrom a measuring device

The number should also be as precise as the measurement!The number should also be as precise as the measurement!

Page 5: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

The International System of Units

• In the signs shown here, the distances are listed as numbers with no units attached. Without the units, it is impossible to communicate the measurement to others. When you make a measurement, you must assign the correct units to the numerical value.

Page 6: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

SI measurementSI measurement• Le Système international Le Système international

d'unitésd'unités • The only countries that have not The only countries that have not

officiallyofficially adopted SI are Liberia adopted SI are Liberia (in western Africa) and Myanmar (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but (a.k.a. Burma, in SE Asia), but now these are reportedly using now these are reportedly using metric regularlymetric regularly

• Metrication is a process that Metrication is a process that does not happen all at once, but does not happen all at once, but is rather a process that happens is rather a process that happens over time. over time.

• In the Philippines, the metric In the Philippines, the metric system was adopted since system was adopted since January of 1983 (Cardenas, January of 1983 (Cardenas, 2010)2010)

Information from U.S. Metric Association

Page 7: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Standards of MeasurementStandards of Measurement

When we measure, we use a measuring tool to When we measure, we use a measuring tool to compare some dimension of an object to a standard.compare some dimension of an object to a standard.

For example, at one time the For example, at one time the standard for length was the standard for length was the king’s foot. What are some king’s foot. What are some

problems with this standard?problems with this standard?

Page 8: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

International System of Units

Measurements depend upon units that serve as reference standards

The standards of measurement used in science are those of the Metric System

Page 9: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

International System of Units

Metric system is now revised and named as the International System of Units (SI), as of 1960

It has simplicity, and is based on 10 or multiples of 10

7 base units, but only five commonly used in chemistry: meter, kilogram, kelvin, second, and mole.

Page 10: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

UNITS OF UNITS OF MEASUREMENTMEASUREMENT

The five SI base units commonly used by chemists are the meter, the kilogram, the kelvin, the second, and the mole.

Page 11: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

International System of Units

Sometimes, non-SI units are usedLiter, Celsius, calorie

Some are derived unitsThey are made by joining other unitsSpeed = miles/hour (distance/time)Density = grams/mL (mass/volume)

Page 12: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Volume – a derived unit

The space occupied by any sample of matter.

Calculated for a solid by multiplying the length x width x height; thus derived from units of length.

SI unit = cubic meter (m3) Everyday unit = Liter (L), which is non-

SI. (Note: 1mL = 1cm3)

Page 13: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

» The volume of 20 drops of liquid from a medicine dropper is approximately 1 mL.

» A sugar cube has a volume of 1 cm3. 1 mL is the same as 1 cm3.

Page 14: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Mass vs. WeightMass vs. Weight

• Mass: Amount Mass: Amount of Matter (grams, of Matter (grams, measured with a measured with a BALANCE)BALANCE)

• Weight: Force Weight: Force exerted by the exerted by the mass, only mass, only present with present with gravity (pounds, gravity (pounds, measured with a measured with a SCALE)SCALE)

Can you hear Can you hear me now?me now?

Page 15: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Some Tools for Some Tools for MeasurementMeasurement

Which tool(s) Which tool(s) would you use to would you use to measure:measure:

A.A. temperature temperature

B.B. volume volume

C.C. time time

D.D. weight weight

Page 16: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning Check

Match Match L) lengthL) length M) mass M) mass V) volume V) volume

____ A. A bag of tomatoes is 4.6 kg.____ A. A bag of tomatoes is 4.6 kg.

____ B. A person is 2.0 m tall.____ B. A person is 2.0 m tall.

____ C. A medication contains 0.50 g Aspirin.____ C. A medication contains 0.50 g Aspirin.

____ D. A bottle contains 1.5 L of water.____ D. A bottle contains 1.5 L of water.

M

L

M

V

Page 17: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning CheckLearning Check

What are some S.I. units that are used to What are some S.I. units that are used to measure each of the following?measure each of the following?

A. Length A. Length

B. volume B. volume

C. weightC. weight

D. temperatureD. temperature

- Meter

- m3

- kg

- K

Page 18: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Metric PrefixesMetric Prefixes• Kilo-Kilo- means 1000 of that unit means 1000 of that unit

– 1 kilometer (km) = 1000 meters (m)1 kilometer (km) = 1000 meters (m)

• Centi-Centi- means 1/100 of that unit means 1/100 of that unit

– 1 meter (m) = 100 centimeters (cm)1 meter (m) = 100 centimeters (cm)

– 1 dollar = 100 cents1 dollar = 100 cents

• Milli-Milli- means 1/1000 of that unit means 1/1000 of that unit

– 1 Liter (L) = 1000 milliliters (mL)1 Liter (L) = 1000 milliliters (mL)

Page 19: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Metric PrefixesMetric Prefixes

Page 20: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Metric PrefixesMetric Prefixes

Page 21: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

1. 1000 m = 1 1. 1000 m = 1 ____ a) mm b) km c) dma) mm b) km c) dm

2. 0.001 g = 1 2. 0.001 g = 1 ___ ___ a) mg b) kg c) dga) mg b) kg c) dg

3. 0.1 L = 1 3. 0.1 L = 1 ______ a) mL b) cL c) dLa) mL b) cL c) dL

4. 0.01 m = 1 ___ 4. 0.01 m = 1 ___ a) mm b) cm c) dma) mm b) cm c) dm

Learning Check

km

mg

cm

dL

Page 22: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning Check

Select the unit you would use to measure Select the unit you would use to measure

1. Your height1. Your height

a) millimeters a) millimeters b) metersb) meters c) kilometers c) kilometers

2. Your mass2. Your mass

a) milligramsa) milligrams b) gramsb) grams c) kilograms c) kilograms

3. The distance between two cities3. The distance between two cities

a) millimetersa) millimeters b) metersb) meters c) kilometers c) kilometers

4. The width of an artery4. The width of an arterya) millimetersa) millimeters b) metersb) meters c) kilometers c) kilometers

Page 23: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Conversion FactorsConversion Factors

Fractions in which the numerator and Fractions in which the numerator and denominator are EQUAL quantities expressed denominator are EQUAL quantities expressed in different unitsin different units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm

2.54 cm 1 in.

Page 24: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning Check

Write conversion factors that relate each of Write conversion factors that relate each of the following pairs of units:the following pairs of units:

1. Liters and mL1. Liters and mL

2. Hours and minutes2. Hours and minutes

3. Meters and kilometers3. Meters and kilometers

1hr60 min

1L1000mL

1000mL1L

60 min1hr

1000m1km

1km1000m

Page 25: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

How many minutes are in 2.5 hours?

Conversion factor

2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min

1 hr1 hr

cancel

By using dimensional analysis / factor-label method, By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the side up, and the UNITS are calculated as well as the

numbers!numbers!

Page 26: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Steps to Problem SolvingSteps to Problem Solving1. Write down the given amount. Don’t forget the units!2. Multiply by a fraction.3. Use the fraction as a conversion factor. Determine if

the top or the bottom should be the same unit as the given so that it will cancel.

4. Put a unit on the opposite side that will be the new unit. If you don’t know a conversion between those units directly, use one that you do know that is a step toward the one you want at the end.

5. Insert the numbers on the conversion so that the top and the bottom amounts are EQUAL, but in different units.

6. Multiply and divide the units (Cancel).7. If the units are not the ones you want for your

answer, make more conversions until you reach that point.

8. Multiply and divide the numbers. Don’t forget “Please Excuse My Dear Aunt Sally”! (order of operations)

Page 27: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning Check

A rattlesnake is 2.44 m long. How A rattlesnake is 2.44 m long. How long is the snake in cm?long is the snake in cm?

a) a) 2440 cm2440 cm

b)b) 244 cm244 cm

c)c) 24.4 cm24.4 cm

Page 28: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Solution

A rattlesnake is 2.44 m long. How A rattlesnake is 2.44 m long. How long is the snake in cm?long is the snake in cm?

b)b) 244 cm244 cm

2.44 m x 2.44 m x 100 cm 100 cm = 244 cm= 244 cm

1 m

Page 29: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning Check

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x 24 hr x ?? 1 day

Page 30: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Wait a minute!

What is What is wrongwrong with the following setup? with the following setup?

1.4 day x 1.4 day x 1 day 1 day x x 60 min 60 min x x 60 sec 60 sec

24 hr 1 hr 1 min24 hr 1 hr 1 min

1.4 day x 1.4 day x 24hr 24hr x x 60 min 60 min x x 60 sec 60 sec = 120, 960sec = 120, 960sec1day 1 hr 1 min1day 1 hr 1 min

Page 31: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

English and Metric English and Metric ConversionsConversions

• If you know ONE conversion for If you know ONE conversion for each type of measurement, you each type of measurement, you can convert anything!can convert anything!

• You must You must memorizememorize and use these and use these conversions:conversions:

–Mass: 454 grams = 1 poundMass: 454 grams = 1 pound

–Length: 2.54 cm = 1 inchLength: 2.54 cm = 1 inch

–Volume: 0.946 L = 1 quartVolume: 0.946 L = 1 quart

Page 32: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning CheckLearning Check

An adult human has 4.65 L of blood. How An adult human has 4.65 L of blood. How many gallons of blood is that?many gallons of blood is that?

Unit plan: L qt gallon

Equalities: 1 quart = 0.946 L

1 gallon = 4 quarts

Your Setup:

4.65L x 4.65L x 1qt 1qt x x 1gallon 1gallon = 1.23gallon = 1.23gallon0.946L 4qt 0.946L 4qt

Page 33: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Steps to Problem SolvingSteps to Problem Solving

Read problemRead problem Identify data Identify data Make a unit plan from the initial unit to the Make a unit plan from the initial unit to the

desired unitdesired unit Select conversion factorsSelect conversion factors Change initial unit to desired unitChange initial unit to desired unit Cancel units and checkCancel units and check Do math on calculator Do math on calculator Give an answer using significant figuresGive an answer using significant figures

Page 34: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Dealing with Two Units Dealing with Two Units

If your pace on a treadmill is 65 meters If your pace on a treadmill is 65 meters per minute, how many seconds will it per minute, how many seconds will it take for you to walk a distance of 8450 take for you to walk a distance of 8450 feet?feet?

Conversion: 1Feet = 0.30m

My Answer is: 2,340sec. Show your solution

Page 35: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

What about Square and Cubic What about Square and Cubic units? – Honors Onlyunits? – Honors Only

• Use the conversion factors you already Use the conversion factors you already know, but when you square or cube the know, but when you square or cube the unit, don’t forget to cube the number unit, don’t forget to cube the number also!also!

• Best way: Square or cube the ENTIRE Best way: Square or cube the ENTIRE conversion factorconversion factor

• Example: Convert 4.3 cmExample: Convert 4.3 cm33 to mm to mm33

4.3 cm4.3 cm33 10 mm 10 mm 33

1 cm 1 cm ( ) =

4.3 cm4.3 cm33 10 1033 mm mm33

1133 cm cm33

= 4300 mm3

Page 36: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning CheckLearning Check

• A Nalgene water A Nalgene water bottle holds 1000 bottle holds 1000 cmcm33 of dihydrogen of dihydrogen monoxide monoxide (DHMO). How (DHMO). How many cubic many cubic decimeters is decimeters is that?that?

Page 37: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

SolutionSolution

1000 cm1000 cm33 1 dm 1 dm 33

10 cm10 cm( ) = 1 dm= 1 dm33

So, a dmSo, a dm33 is the same as a Liter ! is the same as a Liter !

A cmA cm33 is the same as a milliliter. is the same as a milliliter.

Page 38: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Temperature ScalesTemperature Scales• FahrenheitFahrenheit

• CelsiusCelsius

• KelvinKelvin

Anders Celsius1701-1744

Lord Kelvin(William Thomson)1824-1907

Page 39: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Temperature ScalesTemperature Scales

Notice that 1 kelvin = 1 degree Celsius1 kelvin = 1 degree Celsius

Boiling point Boiling point of waterof water

Freezing point Freezing point of waterof water

CelsiusCelsius

100 ˚C100 ˚C

0 ˚C0 ˚C

100˚C100˚C

KelvinKelvin

373 K373 K

273 K273 K

100 K100 K

FahrenheitFahrenheit

32 ˚F32 ˚F

212 ˚F212 ˚F

180˚F180˚F

Page 40: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Calculations Calculations Using Using TemperatureTemperature

• Generally require temp’s in Generally require temp’s in kelvinskelvins

• T (K) = t (˚C) + 273.15T (K) = t (˚C) + 273.15

• Body temp = 37 ˚C + 273 = 310 KBody temp = 37 ˚C + 273 = 310 K

• Liquid nitrogen = -196 ˚C + 273 = 77 KLiquid nitrogen = -196 ˚C + 273 = 77 K

• Generally require temp’s in Generally require temp’s in kelvinskelvins

• T (K) = t (˚C) + 273.15T (K) = t (˚C) + 273.15

• Body temp = 37 ˚C + 273 = 310 KBody temp = 37 ˚C + 273 = 310 K

• Liquid nitrogen = -196 ˚C + 273 = 77 KLiquid nitrogen = -196 ˚C + 273 = 77 K

Page 41: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Fahrenheit Formula Fahrenheit Formula

180°F180°F = = 9°F 9°F == 1.8°F 1.8°F 100°C 100°C 5°C 5°C 1°C1°C

Zero point: 0°C = 32°FZero point: 0°C = 32°F

°F = 9/5 °C + 32°F = 9/5 °C + 32

Page 42: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Celsius Formula Celsius Formula

Rearrange to find T°CRearrange to find T°C

°F °F = = 9/5 °C + 329/5 °C + 32

°F - 32 = °F - 32 = 9/5 °C ( +32 - 32)9/5 °C ( +32 - 32)

°F - 32°F - 32 = = 9/5 °C9/5 °C

9/5 9/5 9/5 9/5

(°F - 32) * 5/9 = (°F - 32) * 5/9 = °C°C

Page 43: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Temperature Conversions Temperature Conversions

A person with hypothermia has a body A person with hypothermia has a body temperature of 29.1°C. What is the body temperature of 29.1°C. What is the body temperature in °F? temperature in °F?

°F °F = = 9/5 (29.1°C) + 329/5 (29.1°C) + 32

= = 52.4 + 3252.4 + 32

= = 84.4°F84.4°F

Page 44: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning Check – Honors OnlyLearning Check – Honors Only

The normal temperature of a chickadee is The normal temperature of a chickadee is 105.8°F. What is that temperature in °C?105.8°F. What is that temperature in °C?

1) 73.8 °C 1) 73.8 °C

2) 58.8 °C2) 58.8 °C

3) 41.0 °C3) 41.0 °C

Page 45: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning Check – Honors Only

Pizza is baked at 455°F. What is that in °C?

1) 437 °C1) 437 °C

2) 235°C2) 235°C

3) 221°C3) 221°C

Page 46: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

–3. A temperature of 30 degrees Celsius is equivalent to

»303 K.

»300 K.

»243 K.

»247 K.

Page 47: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Three Three targets with targets with three arrows three arrows each to each to shoot.shoot.

Can you hit the bull's-eye?Can you hit the bull's-eye?

Both accurate and precise

Precise but not accurate

Neither accurate nor precise

How do How do they they compare?compare?

Can you define accuracy and precision?Can you define accuracy and precision?

Page 48: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Accuracy, Precision, and Error

It is necessary to make good, reliable measurements in the lab

Accuracy – how close a measurement is to the true value

Precision – how close the measurements are to each other (reproducibility)

How is this related with significant figures?

- The greater the number of significant digits, the more precise the measurement and the lower the degree of uncertainty

Page 49: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Significant FiguresSignificant Figures

The numbers reported in a The numbers reported in a measurement are limited by the measurement are limited by the measuring toolmeasuring tool

Significant figures in a Significant figures in a measurement include the known measurement include the known digits plus one estimated digitdigits plus one estimated digit

Page 50: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Reading a MeterstickReading a Meterstick

. l. l22. . . . I . . . . I. . . . I . . . . I33 . . . .I . . . . I . . . .I . . . . I44. . cm. . cm

First digit (known)First digit (known) = 2 = 2 2.?? cm2.?? cm

Second digit (known)Second digit (known) = 0.7 = 0.7 2.7? cm2.7? cm

Third digit (estimated) between 0.05- 0.07Third digit (estimated) between 0.05- 0.07

Length reportedLength reported == 2.75 cm 2.75 cm

oror 2.74 cm 2.74 cm

oror 2.76 cm2.76 cm

Page 51: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Known + Estimated DigitsKnown + Estimated Digits

In 2.76 cm…In 2.76 cm…

• Known digitsKnown digits 2 andand 7 are 100% certainare 100% certain

• The third digit 6 is estimated (uncertain)The third digit 6 is estimated (uncertain)

• In the reported length, all three digits In the reported length, all three digits (2.76 cm) are significant including the (2.76 cm) are significant including the estimated oneestimated one

Page 52: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Counting Significant FiguresCounting Significant Figures

RULE 1. All non-zero digits in a measured number RULE 1. All non-zero digits in a measured number are significant. Only a zero could indicate that are significant. Only a zero could indicate that rounding occurred.rounding occurred.

Number of Significant Figures

38.15 cm38.15 cm 44

5.6 ft5.6 ft 22

65.6 lb65.6 lb ______

122.55 m122.55 m ___

Page 53: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Leading ZerosLeading Zeros

RULE 2. Leading zeros in decimal numbers are RULE 2. Leading zeros in decimal numbers are

NOTNOT significant. Only zeros at the right end of significant. Only zeros at the right end of

the number is significant if decimal is presentthe number is significant if decimal is presentNumber of Significant Figures

0.008 mm0.008 mm 11

0.0150 oz0.0150 oz 33

0.0042 lb0.0042 lb ________

0.000262 mL 0.000262 mL ____

Page 54: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Sandwiched ZerosSandwiched Zeros

RULE 3. Zeros between nonzero numbers are significant. RULE 3. Zeros between nonzero numbers are significant.

(They can not be rounded unless they are on an end of a (They can not be rounded unless they are on an end of a

number.)number.)

Number of Significant Figures

50.8 mm50.8 mm 33

2001 min2001 min 44

0.702 lb0.702 lb ________

0.00405 m0.00405 m ____

Page 55: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Trailing ZerosTrailing Zeros

RULE 4. Trailing zeros in numbers without RULE 4. Trailing zeros in numbers without

decimals are NOT significant. They are only decimals are NOT significant. They are only

serving as place holders.serving as place holders.

Number of Significant Figures

25,000 in. 25,000 in. 22

200. yr200. yr 33

48,600 gal48,600 gal ________

25,005,000 g 25,005,000 g ________

Page 56: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning CheckLearning Check

A. Which answers contain 3 significant figures?A. Which answers contain 3 significant figures?

1) 0.47601) 0.4760 2) 0.00476 2) 0.00476 3) 4760 3) 4760

B. All the zeros are significant inB. All the zeros are significant in

1) 0.00307 1) 0.00307 2) 25.300 2) 25.300 3) 2.050 x 10 3) 2.050 x 1033

C. 534,675 rounded to 3 significant figures isC. 534,675 rounded to 3 significant figures is

1) 535 1) 535 2) 535,000 2) 535,000 3) 5.35 x 10 3) 5.35 x 1055

Page 57: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning CheckLearning Check

In which set(s) do both numbers In which set(s) do both numbers contain the contain the samesame number of number of significant figures?significant figures?

1) 22.0 and 22.00 1) 22.0 and 22.00

2) 400.0 and 40 2) 400.0 and 40

3) 0.000015 and 150,0003) 0.000015 and 150,000

Page 58: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

State the number of significant figures in each of the State the number of significant figures in each of the following:following:

A. 0.030 mA. 0.030 m 1 1 2 2 3 3

B. 4.050 LB. 4.050 L 2 2 3 3 4 4

C. 0.0008 gC. 0.0008 g 1 1 2 2 4 4

D. 3.00 mD. 3.00 m 1 1 2 2 3 3

E. 2,080,000 beesE. 2,080,000 bees 3 3 5 5 7 7

Learning CheckLearning Check

Page 59: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Significant Numbers in CalculationsSignificant Numbers in Calculations

A calculated answer cannot be more precise than A calculated answer cannot be more precise than the measuring tool. the measuring tool.

A calculated answer must match the least precise A calculated answer must match the least precise measurement.measurement.

Significant figures are needed for final answers Significant figures are needed for final answers fromfrom

1) adding or subtracting1) adding or subtracting

2) multiplying or dividing2) multiplying or dividing

Page 60: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Adding and SubtractingAdding and Subtracting

The answer has the same number of decimal The answer has the same number of decimal places as the measurement with the fewest places as the measurement with the fewest decimal places.decimal places.

25.25.22 one decimal placeone decimal place

+ 1.+ 1.3434 two decimal placestwo decimal places

26.5426.54

answer 26.5answer 26.5 one decimal placeone decimal place

Page 61: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning CheckLearning Check

In each calculation, round the answer to the In each calculation, round the answer to the correct number of significant figures.correct number of significant figures.

A. 235.05 + 19.6 + 2.1 = A. 235.05 + 19.6 + 2.1 =

1) 256.751) 256.75 2) 256.8 2) 256.8 3) 2573) 257

B. 58.925 - 18.2B. 58.925 - 18.2 ==

1) 40.7251) 40.725 2) 40.73 2) 40.73 3) 40.73) 40.7

Page 62: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Multiplying and Dividing

Round (or add zeros) to the calculated Round (or add zeros) to the calculated answer until you have the same number answer until you have the same number of significant figures as the measurement of significant figures as the measurement with the fewest significant figures.with the fewest significant figures.

Page 63: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning CheckLearning Check

A. 2.19 X 4.2 =A. 2.19 X 4.2 = 1) 91) 9 2) 9.2 2) 9.2 3) 9.1983) 9.198

B. 4.311 ÷ 0.070 =B. 4.311 ÷ 0.070 = 1)1) 61.5861.58 2) 62 2) 62 3) 603) 60

C. C. 2.54 X 0.00282.54 X 0.0028 = =

0.0105 X 0.060 0.0105 X 0.060

1) 11.31) 11.3 2) 112) 11 3) 0.041 3) 0.041

Page 64: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

What is Scientific Notation?What is Scientific Notation?

• Scientific notation is a way of Scientific notation is a way of expressing really big numbers or expressing really big numbers or really small numbers.really small numbers.

• For very large and very small For very large and very small numbers, scientific notation is numbers, scientific notation is more concise.more concise.

Page 65: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Scientific notation consists Scientific notation consists of two parts:of two parts:

• A number between 1 and 10A number between 1 and 10

• A power of 10A power of 10

N x 10N x 10xx

Page 66: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

To change standard form To change standard form to scientific notation…to scientific notation…

• Place the decimal point so that there is Place the decimal point so that there is one non-zero digit to the left of the one non-zero digit to the left of the decimal point.decimal point.

• Count the number of decimal places Count the number of decimal places the decimal point has “moved” from the decimal point has “moved” from the original number. This will be the the original number. This will be the exponent on the 10.exponent on the 10.

• If the original number was less than 1, If the original number was less than 1, then the exponent is negative. If the then the exponent is negative. If the original number was greater than 1, original number was greater than 1, then the exponent is positive.then the exponent is positive.

Page 67: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

ExamplesExamples

• Given: 289,800,000Given: 289,800,000

• Use: 2.898 (moved 8 places)Use: 2.898 (moved 8 places)

• Answer:Answer: 2.898 x 102.898 x 1088

• Given: 0.000567Given: 0.000567

• Use: 5.67 (moved 4 places)Use: 5.67 (moved 4 places)

• Answer:Answer: 5.67 x 105.67 x 10-4-4

Page 68: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

To change scientific To change scientific notation to standard notation to standard

form…form…• Simply move the decimal point to Simply move the decimal point to

the right for positive exponent 10. the right for positive exponent 10.

• Move the decimal point to the left Move the decimal point to the left for negative exponent 10.for negative exponent 10.

(Use zeros to fill in places.)(Use zeros to fill in places.)

Page 69: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

ExampleExample

• Given: 5.093 x 10Given: 5.093 x 1066

• Answer: Answer: 5,093,0005,093,000 (moved 6 places (moved 6 places to the right)to the right)

• Given: 1.976 x 10Given: 1.976 x 10-4-4

• Answer: Answer: 0.00019760.0001976 (moved 4 places (moved 4 places to the left)to the left)

Page 70: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Learning Check

• Express these numbers in Express these numbers in Scientific Notation:Scientific Notation:

1)1) 405789405789

2)2) 0.0038720.003872

3)3) 30000000003000000000

4)4) 22

5)5) 0.4782600.478260

Page 71: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Rounding Numbers

• All numbers from a measurement are significant. However, we often generate nonsignificant digits when performing calculations.

• We get rid of nonsignificant digits by rounding off numbers.

• There are four rules for rounding off numbers.

Page 72: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Rules for Rounding Numbers

1. If the first nonsignificant digit is less than 5, drop all nonsignificant digits.

Example:

A calculator displays 12.846239 and 3 significant digits are justified.

The first nonsignificant digit is a 4, so we drop all nonsignificant digits and get 12.8 as the answer.

Page 73: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

2. If the first nonsignificant digit is greater than 5, increase the last significant digit by 1 and drop all nonsignificant digits.

A calculator display 12.865239 and 3 significant digits are justified.

The first nonsignificant digit is a 6, so the last significant digit is increased by one to 9, all the nonsignificant digits are dropped, and we get 12.9 as the answer.

Rules for Rounding Numbers

Page 74: Chapter 2 “Scientific Measurement” OBJECTIVES: -Determine the fundamental units of SI -Convert measurements to various units and scientific notation

Rounding Numbers

3. a) If the last digit is 5 and is preceded by an odd number, then the last digit should be increased by 1.

Example: 4.635 is rounded to 4.64

b) If the last digit is 5 but is preceded by an even number, then it stays the same or is rounded down by 1.

Example: 4.625 is rounded to 4.62.

4. If a calculation has two or more operations, retain all nonsignificant digits until the final operation and then round off the answer.