SCIENTIFIC MEASUREMENT

CHEM IH: CHAPTER 3

What is Scientific What is Scientific Notation?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.

Scientific notation consists of Scientific notation consists of two parts: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

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 108 8 (how many (how many

sig figs? Honors only)sig figs? Honors only)

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 (How many sig (How many sig

figs? Honors only)figs? Honors only)

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 number should also be as precise as

the measuring device.the measuring device.

Ex: Reading a MeterstickEx: Reading 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

UNITS OF MEASUREMENTUNITS OF MEASUREMENT

Use Use SI unitsSI units — based on the metric — based on the metric systemsystem

Length Length

MassMass

VolumeVolume

TimeTime

TemperatureTemperature

Meter, mMeter, m

Kilogram, kgKilogram, kg

Seconds, sSeconds, s

Celsius degrees, ˚CCelsius degrees, ˚Ckelvins, Kkelvins, K

Liter, LLiter, L

Metric PrefixesMetric Prefixes

Significant Figures (Honors only)Significant Figures (Honors only)

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 digits plus one estimated digitplus one estimated digit

Counting Significant Figures: Counting Significant Figures: Non-Zero Digits (Honors Only)Non-Zero Digits (Honors Only)

RULE 1. All non-zero digits in a measured RULE 1. All non-zero digits in a measured number ARE significant. number ARE significant.

#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 ___

Counting Significant Figures:Counting Significant Figures:Leading Zeros (Honors Only)Leading Zeros (Honors Only)

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

are are NOTNOT significant. significant.

#of Significant Figures

0.008 mm0.008 mm 11

0.0156 oz0.0156 oz 33

0.0042 lb0.0042 lb ________

0.000262 mL 0.000262 mL ____

Counting Significant Figures:Counting Significant Figures:Sandwiched Zeros (Honors Only)Sandwiched Zeros (Honors Only)

RULE 3. Zeros between nonzero numbers RULE 3. Zeros between nonzero numbers

ARE significant. (They can not be rounded ARE significant. (They can not be rounded

unless they are on an end of a number.)unless they are on an end of a number.)# of Significant Figures

50.8 mm50.8 mm 33

2001 min2001 min 44

0.702 lb0.702 lb ________

0.00405 m0.00405 m ____

Counting Significant Figures:Counting Significant Figures:Zeros @ the End of a # & to the Right Zeros @ the End of a # & to the Right of a Decimal of a Decimal (Honors Only)(Honors Only)

RULE 4. Trailing zeros at the end of a number RULE 4. Trailing zeros at the end of a number

and to the right of a decimal numbers ARE and to the right of a decimal numbers ARE

significant. significant.

# # of Significant Figures

43.00 m. 43.00 m. 44

200.00 yr200.00 yr 55

1.10 gal1.10 gal ________

0.04500 g 0.04500 g ________

Counting Significant Figures:Counting Significant Figures:Trailing Zeros (Honors Only)Trailing Zeros (Honors Only)

RULE 5. Trailing zeros in numbers without RULE 5. Trailing zeros in numbers without

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

only serving as place holders.only serving as place holders.

# 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 ________

Counting Significant Figures:Counting Significant Figures:Unlimited Sig Figs (Honors Only)Unlimited Sig Figs (Honors Only)

RULE 6. 2 instances in which there are an RULE 6. 2 instances in which there are an

unlimited # of sig figs.unlimited # of sig figs.

a)a)CountingCounting. Ex: 23 people in our classroom. . Ex: 23 people in our classroom.

b)b)Exactly defined quantities.Exactly defined quantities. Ex: 1hr = 60 Ex: 1hr = 60

min.min.

Both are exact values. There is no uncertainty.

Neither of these types of values affect the Neither of these types of values affect the

process of rounding an answerprocess of rounding an answer..

Shortcuts to Sig FigsThe Atlantic-Pacific Rule says:

"If a decimal point is Present, ignore zeros on the Pacific (left) side.

If the decimal point is Absent, ignore zeros on the Atlantic (right) side.

Everything else is significant."

Learning Check (Honors Only)Learning Check (Honors Only)

A. Which answers contain 3 significant A. Which answers contain 3 significant figures?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 3) 2.050 x 101033

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

Learning Check Learning Check (Honors Only)(Honors Only)

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

Significant Numbers in Calculations Significant Numbers in Calculations (Honors Only)(Honors Only)

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

A calculated answer must match the A calculated answer must match the least least precise 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 If you must round to obtain the right # of sig If you must round to obtain the right # of sig

figs, do so figs, do so after all calcs are completeafter all calcs are complete

Adding and Subtracting (Honors Adding and Subtracting (Honors Only)Only)

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

Learning Check (Honors Only)Learning Check (Honors Only)

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

Multiplying and Dividing (Honors (Honors Only)Only)

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

Learning Check (Honors Only)Learning Check (Honors Only)

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 ÷ 0.07 =B. 4.311 ÷ 0.07 = 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

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 hr. = 60 min

Factors: 1 hr. and 60 min60 min 1 hr.

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

Learning Check

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x 24 hr x _60min x 60 s =

1 day 1 hr 1 min

ANSWER: 120,960 s.FINAL ANSWER (in sig figs) = 120,000 s

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