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What is the Length?

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- 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

What is the length of the wooden stick?

1) 4.5 cm

2) 4.58 cm

3) 4.584 cm

Chapter Two

- 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.

- Find your Notecard Partner.
- Why would we use scientific notation?

SCIENTIFIC NOTATION

A QUICK WAY TO WRITE

REALLY, REALLY BIG

OR

REALLY, REALLY SMALLNUMBERS.

- # 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

- 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

- 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

- 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

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

- 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

???

- 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!

- 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

Leading zero

Captive zeros

114.20 - five significant figures

Trailing zero

???

- Leading zeros are notsignificant.
- Captive zeros are always significant!

???

Trailing zeros are significant …

IF there’s a decimal point in the number!

???

- 250 mg
- \__ 2 significant figures
- 120. miles
- \__ 3 significant figures
- 0.00230 kg
- \__ 3 significant figures
- 23,600.01 s
- \__ 7 significant figures

- 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

- 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?

- Example

0.333333

speed = 1.0 km

3.0 min

= 0.33 km

min

ONLY 3 SIG FIGS!

ONLY 2 SIG FIGS!

- 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

- 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.

- 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 -

2.5795035 becomes 2.580

34.204221 becomes 34.20

1st insignificant digit

- 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.

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

3.2650106 4.858 = 1.586137 107

6.0221023 1.66110-24= 1.000000