# What is the Length? - PowerPoint PPT Presentation

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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?

• 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?

1) 4.5 cm

2) 4.58 cm

3) 4.584 cm

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

• Find your Notecard Partner.

• Why would we use scientific notation?

## SCIENTIFIC NOTATION

A QUICK WAY TO WRITE

REALLY, REALLY BIG

OR

REALLY, REALLY SMALLNUMBERS.

### 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

• 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 =

0.0000187

370,000,000

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 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

• 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

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

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 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

• 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!

4,008 - four significant figures

0.421 - three significant figures

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

• 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

• 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

• 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

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

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

• 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

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

• 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

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