Transcript
Page 1: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Measurement

• 100 mL Graduated Cylinder• Units of Measuring Volume• Reading a Meniscus• Units for Measuring Mass• Quantities of Mass• SI-English Conversion Factors• Accuracy vs. Precision• Accuracy Precision Resolution• SI units for Measuring Length• Comparison of English and SI Units• Reporting Measurements• Measuring a Pin• Practice Measuring

Page 2: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Measurement• 100 mL Graduated Cylinder• Units of Measuring Volume• Reading a Meniscus• Units for Measuring Mass• Quantities of Mass• SI-English Conversion Factors• Accuracy vs. Precision• Accuracy Precision Resolution• SI units for Measuring Length• Comparison of English and SI Units• Reporting Measurements• Measuring a Pin• Practice Measuring

Page 3: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

100 mL Graduated Cylinder

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119

Page 4: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Instruments for Measuring Volume

Graduatedcylinder

Syringe Volumetric flaskBuret Pipet

Page 5: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Units of Measuring Volume

1 L = 1000 mL

1 qt = 946 mL

Timberlake, Chemistry 7th Edition, page 3

Page 6: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Reading a Meniscus

10

8

6

line of sight too high

reading too low

reading too high

line of sight too low

proper line of sightreading correct

graduatedcylinder

10 mL

Page 7: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Christopherson Scales

Made in Normal, Illinois USA

Units for Measuring Mass

1 kg = 2.20 lb

1 kg(1000 g) 1 lb 1 lb

0.20 lb

Page 8: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Quantities of Mass

Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25

Earth’s atmosphere to 2500 km

Ocean liner

Indian elephant

Average human

1.0 liter of water

Grain of table salt

Typical protein

Uranium atomWater molecule

1024 g

1021 g

1018 g

1015 g

1012 g

109 g

106 g

103 g

100 g

10-3 g

10-6 g

10-9 g

10-12 g

10-15 g

10-18 g

10-21 g

10-24 g

Giga- Mega-

Kilo-Kilo-

base

milli-milli-

micro-

nano-

pico-

femto-

atomo-

Page 9: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Factor Name Symbol Factor Name Symbol

10-1 decimeter dm 101 decameter dam

10-2 centimeter cm 102 hectometer hm

10-3 millimeter mm 103 kilometer km

10-6 micrometer m 106 megameter Mm

10-9 nanometer nm 109 gigameter Gm

10-12 picometer pm 1012 terameter Tm

10-15 femtometer fm 1015 petameter Pm

10-18 attometer am 1018 exameter Em

10-21 zeptometer zm 1021 zettameter Zm

10-24 yoctometer ym 1024 yottameter Ym

Page 10: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Scientific Notation:  Powers of Ten

Rules for writing numbers in scientific notation:

Write all significant figures but only the significant figures.

Place the decimal point after the first digit, making the number have a value between 1 and 10. Use the correct power of ten to place the decimal point properly, as indicated below.         a)  Positive exponents push the decimal point to the right.  The number becomes larger.              It is multiplied by the power of 10.        b)  Negative exponents push the decimal point to the left.  The number becomes smaller.              It is divided by the power of 10.        c)  10o  =  1

                    Examples:    3400  =  3.20 x 103                0.0120  =  1.20 x 10-2

Nice visual display of Powers of Ten (a view from outer space to the inside of an atom) viewed by powers of 10!

Page 11: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Multiples of bytesas defined by IEC 60027-2

SI prefix Binary prefixes

Name Symbol Multiple NameSymbol

Multiple

kilobyte kB 103 (or 210) kibibyte KiB 210

megabyte MB 106 (or 220) mebibyte MiB 220

gigabyte GB 109 (or 230) gibibyte GiB 230

terabyte TB 1012 (or 240) tebibyte TiB 240

petabyte PB 1015 (or 250) pebibyte PiB 250

exabyte EB 1018 (or 260) exbibyte EiB 260

zettabyte ZB 1021 (or 270)

yottabyte YB 1024 (or 280)

A yottabyte (derived from the SI prefix )

Page 12: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

SI-US Conversion FactorsRelationship Conversion Factors

Length

Volume

Mass

2.54 cm = 1 in.

1 m = 39.4 in.

946 mL = 1 qt

1 L = 1.06 qt

454 g = 1 lb

1 kg = 2.20 lb

1 in2.54 cm

39.4 in 1 m

1 m 39.4 in.

946 mL 1 qt

1 qt 946 mL

1.06 qt 1 L

1 L 1.06 qt

454 g 1 lb

1 lb 454 g

2.20 lb 1 kg

1 kg 2.20 lb

2.54 cm 1 in and

and

and

and

and

and

Page 13: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Accuracy vs. Precision

Random errors: reduce precision

Good accuracyGood precision

Poor accuracyGood precision

Poor accuracyPoor precision

Systematic errors: reduce accuracy

(person)(instrument)

Page 14: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

                                  

                                                                                        

                            

Precision Accuracy

reproducibility

check by repeating measurements

poor precision results from poor technique

correctness

check by using a different method

poor accuracy results from procedural or equipment flaws.

Page 15: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Types of errors

Systematic

• Instrument not ‘zeroed’ properly

• Reagents made at wrong concentration

Random

• Temperature in room varies ‘wildly’

• Person running test is not properly trained

Page 16: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Errors

SystematicErrors in a single direction (high or low)

Can be corrected by proper calibration or running controls and blanks.

RandomErrors in any direction.

Can’t be corrected. Can only be accounted

for by using statistics.

Page 17: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Accuracy Precision Resolution

subsequent samples

time

off

set

[arb

itrar

y un

its]

not accurate, not precise accurate, not precise not accurate, precise

accurate and precise accurate, low resolution

-2

-3

-1

0

1

2

3

Page 18: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

SI Prefixes

kilo- 1000

deci- 1/10

centi- 1/100

milli- 1/1000

Also know…

1 mL = 1 cm3 and 1 L = 1 dm3

Page 19: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

SI System for Measuring Length

Unit Symbol Meter Equivalent _______________________________________________________________________

kilometer km 1,000 m or 103 m

meter m 1 m or 100 m

decimeter dm 0.1 m or 10-1 m

centimeter cm 0.01 m or 10-2 m

millimeter mm 0.001 m or 10-3 m

micrometer m 0.000001 m or 10-6 m

nanometer nm 0.000000001 m or 10-9 m

The SI Units for Measuring Length

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118

Page 20: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Comparison of English and SI Units

1 inch

2.54 cm

1 inch = 2.54 cmZumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119

Page 21: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Reporting Measurements

• Using significant figures

• Report what is known with certainty

• Add ONE digit of uncertainty (estimation)

Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

Page 22: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Measuring a Pin

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 122

Page 23: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Practice Measuring

4.5 cm

4.54 cm

3.0 cm

Timberlake, Chemistry 7th Edition, page 7

cm0 1 2 3 4 5

cm0 1 2 3 4 5

cm0 1 2 3 4 5

Page 24: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Implied Range of Uncertainty

5 643

Implied range of uncertainty in a measurement reported as 5 cm.

5 643

Implied range of uncertainty in a measurement reported as 5.0 cm.

Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32

5 643

Implied range of uncertainty in a measurement reported as 5.00 cm.

Page 25: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

20

10

?

15 mL ?15.0 mL1.50 x 101 mL

Page 26: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Reading a Vernier

A Vernier allows a precise reading of some value. In the figure to the left, the Vernier moves up and down to measure a position on the scale.

This could be part of a barometer which reads atmospheric pressure.

The "pointer" is the line on the vernier labeled "0". Thus the measured position is almost exactly 756 in whatever units the scale is calibrated in.

If you look closely you will see that the distance between the divisions on the vernier are not the same as the divisions on the scale. The 0 line on the vernier lines up at 756 on the scale, but the 10 line on the vernier lines up at 765 on the scale. Thus the distance between the divisions on the vernier are 90% of the distance between the divisions on the scale.

756

750

760

770

Sca

le 5

0

10V

ern

ier

http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html

Page 27: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately 746.5 on the scale.

If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is 746.5.

5

0

10

750

740

760

What is the reading now? 741.9

http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html

Page 28: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

750

740

760

If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately 746.5 on the scale.

If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is 746.5.

5

0

10

What is the reading now? 756.0

http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html

Page 29: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

750

740

760 Here is a final example, with the vernier at yet another position. The pointer points to a value that is obviously greater than 751.5 and also less than 752.0. Looking for divisions on the vernier that match a division on the scale, the 8 line matches fairly closely. So the reading is about 751.8.

In fact, the 8 line on the vernier appears to be a little bit above the corresponding line on the scale. The 8 line on the vernier is clearly somewhat below the corresponding line of the scale. So with sharp eyes one might report this reading as 751.82 ± 0.02.This "reading error" of ± 0.02 is probably the correct error of precision to specify for all measurements done with this apparatus.

5

0

10

http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html

Page 30: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

How to Read a Thermometer(Celcius)

10

5

0

4.0 oC

10

5

0

8.3 oC

100

50

0

64 oC

5

0

3.5 oC

Page 31: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

0oC

10oC

20oC

30oC

40oC

50oC

60oC

0oC

1oC

2oC

3oC

4oC

5oC

6oC

0oC

5oC

10oC

15oC

20oC

25oC

0oC

20oC

40oC

60oC

80oC

100oC

0oC

20oC

40oC

60oC

80oC

100oC

Record the Temperature(Celcius)

AA BB CC DD EE30.0oC 3.00oC 19.0oC 48oC 60.oC

Page 32: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

MeasurementsMeasurements

Metric (SI) unitsMetric (SI) units PrefixesPrefixes UncertaintyUncertainty

Significant figures

Significant figures

Conversionfactors

Conversionfactors

LengthLength

DensityDensity

MassMass VolumeVolume

Problem solving withconversion factors

Problem solving withconversion factors

Timberlake, Chemistry 7th Edition, page 40

Page 33: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

I

II

III

Using Measurements

MEASUREMENT

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 34: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Accuracy vs. Precision

AccuracyAccuracy - how close a measurement is to the accepted value

PrecisionPrecision - how close a series of measurements are to each other

ACCURATE = Correct

PRECISE = ConsistentCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 35: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Percent Error

Indicates accuracy of a measurement

100literature

literaturealexperimenterror %

your value

accepted valueCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 36: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Percent Error

A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.

100g/mL 1.36

g/mL 1.36g/mL 1.40error %

% error = 2.9 %

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 37: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Significant Figures

Indicate precision of a measurement.

Recording Sig Figs

Sig figs in a measurement include the known digits plus a final estimated digit

2.35 cm

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 38: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Significant Figures

Counting Sig Figs (Table 2-5, p.47)

Count all numbers EXCEPT:

Leading zeros -- 0.0025

Trailing zeros without a decimal point -- 2,500

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 39: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

4. 0.080

3. 5,280

2. 402

1. 23.50

Significant Figures

Counting Sig Fig Examples

1. 23.50

2. 402

3. 5,280

4. 0.080

4 sig figs

3 sig figs

3 sig figs

2 sig figs

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 40: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Significant Figures

Calculating with Sig Figs

Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.

(13.91g/cm3)(23.3cm3) = 324.103g

324 g

4 SF 3 SF3 SF

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 41: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Significant Figures

Calculating with Sig Figs (con’t)

Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g 7.9 mL 350 g

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 42: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Significant Figures

Calculating with Sig Figs (con’t)

Exact Numbers do not limit the # of sig figs in the answer.Counting numbers: 12 studentsExact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 43: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Significant Figures

5. (15.30 g) ÷ (6.4 mL)

Practice Problems

= 2.390625 g/mL

18.1 g

6. 18.9 g

- 0.84 g18.06 g

4 SF 2 SF

2.4 g/mL2 SF

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 44: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Scientific Notation

Converting into scientific notation:

Move decimal until there’s 1 digit to its left. Places moved = exponent.

Large # (>1) positive exponentSmall # (<1) negative exponent

Only include sig. figs.

65,000 kg 6.5 × 104 kg

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 45: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Scientific Notation

7. 2,400,000 g

8. 0.00256 kg

9. 7 10-5 km

10. 6.2 104 mm

Practice Problems

2.4 106 g

2.56 10-3 kg

0.00007 km

62,000 mmCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 46: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Scientific Notation

Calculating with scientific notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.44EXPEXP

EEEE÷÷

EXPEXP

EEEE ENTERENTER

EXEEXE7 8.1 4

= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

Type on your calculator:

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 47: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Proportions

Direct Proportion

Inverse Proportion

xy

xy

1

y

x

y

xCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Page 48: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Reviewing ConceptsMeasurement

• Why do scientists use scientific notation?

• What system of units do scientists use for measurements?

• How does the precision of measurements affect the precision of scientific calculations?

• List the SI units for mass, length, and temperature.

Page 49: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Rules for Counting Significant Figures

1. Nonzero integers always count as significant figures.

2. Zeros: There are three classes of zeroes.

a. Leading zeroes precede all the nonzero digits and DO NOT count assignificant figures. Example: 0.0025 has ____ significant figures.

b. Captive zeroes are zeroes between nonzero numbers. These alwayscount as significant figures. Example: 1.008 has ____ significant figures.

c. Trailing zeroes are zeroes at the right end of the number.

Trailing zeroes are only significant if the number contains a decimal point.Example: 1.00 x 102 has ____ significant figures.

Trailing zeroes are not significant if the number does not contain a decimalpoint. Example: 100 has ____ significant figure.

3. Exact numbers, which can arise from counting or definitions such as 1 in = 2.54 cm, never limit the number of significant figures in a calculation.

2

4

3

1

Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination 2006, page 53

Page 50: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

Significant figures: Rules for zeros

Leading zeros are not significant.

Captive zeros are significant.

Trailing zeros are significant.

Leading zeroLeading zero

Captive zeroCaptive zero

Trailing zeroTrailing zero

0.421

4012

114.20

– three significant figures

– four significant figures

– five significant figures

Page 51: Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors

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