What is the length
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What is the Length?. We can see the markings between 1.6-1.7cm We can ’ t see the markings between the .6-.7 We must guess between .6 & .7 We record 1.67 cm as our measurement The last digit an 7 was our guess.. .stop there. Learning Check. What is the length of the wooden stick?

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What is the Length?

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What is the length

What is the Length?

  • We can see the markings between 1.6-1.7cm

  • We can’t see the markings between the .6-.7

  • We must guess between .6 & .7

  • We record 1.67 cm as our measurement

  • The last digit an 7 was our guess...stop there


Learning check

Learning Check

What is the length of the wooden stick?

1) 4.5 cm

2) 4.58 cm

3) 4.584 cm


Measurement and significant figures

Chapter Two

Measurement 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.


Scientific notation

Scientific Notation

  • Find your Notecard Partner.

  • Why would we use scientific notation?


Scientific notation1

SCIENTIFIC NOTATION

A QUICK WAY TO WRITE

REALLY, REALLY BIG

OR

REALLY, REALLY SMALLNUMBERS.


Scientific notation2

Scientific 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 notation

Rules 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?


What is the length

  • Change to standard form.

  • 1.87 x 10–5 =

  • 3.7 x 108 =

  • 7.88 x 101 =

  • 2.164 x 10–2 =

0.0000187

370,000,000

78.8

0.02164


What is the length

  • 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 units

The International System of Units

  • Lengthmeter m

  • Masskilogram kg

  • Timesecond s

  • Amount of substancemole mol

  • TemperatureKelvin K

  • Electric currentamperes amps

  • Luminous intensitycandela cd

QuantityNameSymbol

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


Si system

SI System

  • The International System of Units

  • Derived Units Commonly Used in Chemistry

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


Need to know prefixes in the si system

NEED TO KNOW Prefixes in the SI System

Power of 10 for

Prefix SymbolMeaning Scientific Notation

_________________________________________________________

mega-M 1,000,000106

kilo-k 1,000103

deci-d 0.110-1

centi-c 0.0110-2

milli-m 0.00110-3

micro-m 0.00000110-6

nano-n 0.00000000110-9

pico-p 0.00000000000110-12


Significant figures

Certain

Digits

Uncertain

Digit

Significant 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

???


Significant figures1

Significant figures

  • The number of significant digits is independent of the decimal point.

    • 255

    • 31.7

    • 5.60

    • 0.934

    • 0.0150

These numbers

All have three

significant figures!


Rules for counting significant figures

Rules for Counting Significant figures

  • Every non-zero digit is ALWAYS significant!

  • Zeros are what will give you a headache!

  • They are used/misused all of the time.

  • SEE p.24 in your book!


Rules for zeros

4,008 - four significant figures

0.421 - three significant figures

Leading zero

Captive zeros

114.20 - five significant figures

Trailing zero

Rules for zeros

???

  • Leading zeros are notsignificant.

  • Captive zeros are always significant!

???

Trailing zeros are significant …

IF there’s a decimal point in the number!

???


Examples

Examples

  • 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 rules for zeros

Significant figures:Rules for zeros

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

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

0.00321 = 3.21 x 10-3

Three Significant

Figures


Significant figures and calculations

Significant figures and calculations

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

    • Example

      • How fast did you run if you

      • went 1.0 km in 3.0 minutes?

0.333333

speed = 1.0 km

3.0 min

= 0.33 km

min


Significant figures and calculations1

ONLY 3 SIG FIGS!

ONLY 2 SIG FIGS!

Significant figures and calculations

  • 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


Significant figures and calculations2

123.45987 g

+ 234.11 g

357.57 g

805.4 g

- 721.67912 g

83.7 g

Significant figures and calculations

  • Addition and subtraction

  • Your answer should have the same number of digits to the right of the decimal point as the number having the fewest to start with.


Rounding off numbers

Rounding 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.


Examples of rounding off

Examples of rounding off

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

2.5795035 becomes 2.580

34.204221 becomes 34.20

1st insignificant digit


Examples of rounding

Examples of Rounding

  • For example you want a 4 Sig Fig number

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

4965.03

780,582

1999.5

4965

780,600

2000.


Multiplication and division

Multiplication and division

49.7

46.4

.05985

1.586 107

1.000

32.27  1.54 = 49.6958

3.68  .07925 = 46.4353312

1.750  .0342000 = 0.05985

3.2650106 4.858 = 1.586137  107

6.0221023 1.66110-24= 1.000000


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