1

What is the Length?

1 2 3 4 cm

We can see the markings between 1.6-1.7cmWe can’t see the markings between the .6-.7We must guess between .6 & .7We record 1.67 cm as our measurementThe last digit an 7 was our guess...stop there

Learning CheckLearning Check

What is the length of the wooden stick?

1) 4.5 cm 2) 4.58 cm 3) 4.584 cm

Measurement and Significant FiguresMeasurement and Significant Figures

Every experimental measurement has a degree of uncertainty.

The volume, V, at right is certain in the 10’s place, 10mL<V<20mL

The 1’s digit is also certain, 17mL<V<18mL

A best guess is needed for the tenths place.

Chapter Two 3

Scientific NotationScientific Notation

Find your Notecard Partner.

Why would we use scientific notation?

SCIENTIFIC NOTATIONSCIENTIFIC NOTATION

A QUICK WAY TO WRITE

REALLY, REALLY BIG OR

REALLY, REALLY SMALL NUMBERS.

Scientific NotationScientific Notation# from 1 to 9.999 x 10exponent

800 = 8 x 10 x 10 = 8 x 102

2531 = 2.531 x 10 x 10 x 10

= 2.531 x 103

0.0014 = 1.4 ÷ 10 ÷ 10 ÷ 10

= 1.4 x 10-3

Rules for Scientific NotationRules for Scientific Notation

To be in proper scientific notation the number must be written with* a number between 1 and 10* and multiplied by a power of

ten 23 X 105 is not in proper scientific notation. Why?

Change to standard form.

1.87 x 10–5 =

3.7 x 108 =

7.88 x 101 =

2.164 x 10–2 =

370,000,000

0.0000187

78.8

0.02164

Change to scientific notation.

12,340 = 0.369 = 0.008 = 1,000. =

1.234 x 104

3.69 x 10–1

8 x 10–3

1.000 x 103

The International System of UnitsThe International System of Units

Length meter m

Mass kilogram kg

Time second s

Amount of substance mole mol

Temperature Kelvin K

Electric current amperes amps

Luminous intensity candela cd

Quantity Name Symbol

Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 16

SI SystemSI SystemThe International System of Units

Derived Units Commonly Used in Chemistry

Map of the world where red represents countries which do not use the metric system

NEED TO KNOW Prefixes in the SI SystemNEED TO KNOW Prefixes in the SI System

Power of 10 for Prefix Symbol Meaning Scientific Notation_________________________________________________________

mega- M 1,000,000 106

kilo- k 1,000 103

deci- d 0.1 10-1

centi- c 0.01 10-2

milli- m 0.001 10-3

micro- 0.000001 10-6

nano- n 0.000000001 10-9

pico- p 0.000000000001 10-12

Significant figuresSignificant figures

Method used to express accuracy and precision.

You can’t report numbers better than the method used to measure them.

67.20 cm = four significant figures

UncertainDigit

Certain Digits

???

Significant figuresSignificant figures

The number of significant digits is independent of the

decimal point.255 31.7 5.60 0.934 0.0150

These numbersAll have three

significant figures!

Rules for Counting Significant figuresRules for Counting Significant figures

Every non-zero digit is Every non-zero digit is ALWAYS significant!ALWAYS significant!

Zeros are what will give Zeros are what will give you a headache!you a headache!

They are used/misused all of the time.

SEE p.24 in your book!

Rules for zerosRules for zerosLeading zeros are notare not significant.

Captive zeros are alwaysare always significant!

0.421 - three significant figuresLeading zeroLeading zero

Trailing zeros areare significant …IFIF there’s a decimal point decimal point in the number!

114.20 - five significant figures

Trailing zeroTrailing zero

???

???

4,008 - four significant figuresCaptive zerosCaptive zeros

???

ExamplesExamples

250 mg

\__ 2 significant figures

120. miles

\__ 3 significant figures

0.00230 kg

\__ 3 significant figures

23,600.01 s

\__ 7 significant figures

Significant figures:Significant figures:Rules for zerosRules for zeros

Scientific notationScientific notation - can be used to clearly express significant figures.

A properly written number in scientific notation always has the proper number of significant figures.

0.00321321 = 3.213.21 x 10-3

Three SignificantFigures

Three SignificantFigures

Significant figures and Significant figures and calculationscalculations

An answer can’t have more significant figures than the quantities used to produce it.

ExampleExampleHow fast did you run if youwent 1.0 km in 3.0 minutes?speed = 1.0 km

3.0 min = 0.33 km

min

0.333333

Significant figures and calculationsSignificant figures and calculations

Multiplication and division.Multiplication and division.

Your answer should have the same number of sig figs as the original number with the smallest number of significant figures.

21.4 cm x 3.095768 cm = 66.2 cm2

135 km ÷ 2.0 hr = 68 km/hr

ONLY 3 SIG FIGS!

ONLY 2 SIG FIGS!

Significant figures and calculationsSignificant figures and calculations

Addition and subtractionAddition and subtractionYour answer should have the same number of digits to the right of the decimal point as the number having the fewest to start with.

123.45987 g+ 234.11 g 357.57 g

805.4 g- 721.67912 g 83.7 g

Rounding off numbersRounding off numbers

After calculations, you may need to round off.

If the first insignificant digit is 5 or more, you round up

If the first insignificant digit is 4 or less, you round down.

If a set of calculations gave you the following numbers and you knew each was supposed to have four significant figures then -

2.57995035 becomes 2.580

34.2004221 becomes 34.20

Examples of rounding offExamples of rounding off

1st insignificant digit1st insignificant digit

Examples of RoundingExamples of Rounding

For example you want a 4 Sig Fig number

4965.03

780,582

1999.5

0 is dropped, it is <5

8 is dropped, it is >5; Note you must include the 0’s

5 is dropped it is = 5; note you need a 4 Sig Fig

4965

780,600

2000.

Multiplication and divisionMultiplication and division

32.27 1.54 = 49.6958

3.68 .07925 = 46.4353312

1.750 .0342000 = 0.05985

3.2650106 4.858 = 1.586137 107

6.0221023 1.66110-24 = 1.000000

49.7

46.4

.05985

1.586 107

1.000