Why do we need it? Because in chemistry we are measuring very small things like protons and electrons and we need an easy way to express these numbers.

Scientific notation expresses numbers as a multiple of two factors: 1)A number between 1 and 10.2)Ten is raised to an exponent and this tells you how many times the factor should be multiplied by ten.

SCIENTIFIC NOTATION

To express a number in scientific notation move the decimal point until after the first digit and count the positions you moved it.

If you move it to the left, you are making the number smaller, so to keep the same number, multiply it by 10 elevated to the positive power of the positions moved.

3,591 = 3.591 X 103

3,591

SCIENTIFIC NOTATION

If you move it to the right, you are making the number bigger, so to keep the same number, multiply it by 10 elevated to the negative power of the positions moved.

0.0000345=

0.0000345

3.45 X 10-5

SCIENTIFIC NOTATION

Summarizing…Summarizing…

• If the number is LARGER than 1 the exponent of 10 is POSITIVE.

• If the number is SMALLER than 1 the exponent of 10 is NEGATIVE.

Practice: 1,222,000,000 =

0.00002035 =

0.9999 =

109 =

100,000 =

 

1.222 x 109

2.035 x 10-5

9.999 x 10-1

1.09 x 102

1 x 105

Convert to scientific notation

More Practice: 25,000,000 =

0.012 =

0.00000001 =

345.9 =

45.803 x 10-5 =

 

2.5 x 107

1.2 x 10-2

1 x 10-8

3.459 x 102

4.5803 x 10-4

More Practice: 1.14 x 104 =

9.08 x 10-4 =

1.112 x 106 =

2.32 x 10-9 =

5.83 x 10-5 =

 

11,400

0.000908

1,112,000

0.00000000232

0.0000583

Convert these to numbers not in scientific notation

Multiplication:

1) Multiply the factors

2) Add the exponents.

Multiplications and divisions with exponential numbers

Example:

2.3 X 103 X 2.0 X 102 =

1.5 X 10-6 X 3.0 X 104 =

2.1 X 10-3 X 4.0 X 10-2 =

4.6 X

4.5 X

8.4 X

105

10-2

10-5

1) Divide the factors

2) Subtract the exponents (numerator – denominator).

Division

Example:2.4 X 103 =

2.0 X 102

6.3 X 10-4 =

3.0 X 102

8.4 X 103 =

4.0 X 10-2

1.2 X

2.1 X

2.1 X

10

10-6

105

Practice:1) 3.4 X 104 =

2.1 X 102

2) 4.3 X 105 X 8.0 X 103=

3) 9.8 X 10-5 =

7.3 X 102

  4) 6.9 X 10-2 X 2.4 X 103=  5) 2.3 X 10-5 X 5.0 X 10-3=

6) 1.7 X 10-5 =

1.4 X 10-6

1.6 x 102

3.4 x 109

1.2 x 10

1.2 x 10-7

1.7 x 102

1.3 x 10-7

Adding and Subtracting in Scientific Adding and Subtracting in Scientific NotationNotation

• You must be sure that the exponents are the SAME.

• Then when you add the non-exponential numbers the exponents stay the same.

• Example:

Base UnitsBase Units

• In science we use _________ which are numbers with __________, because the number alone doesn’t tell you the value of the measurement.

• For example if I measure the length of an object, if I say it is 3.0, it could be as short as 3.0 mm or as long as 3.0 Km therefore I must specify the unit used to compare it.

quantitiesunits

……cont…Base Unitscont…Base Units• Standard units of measurements are

necessary because scientists need to report data that others scientists can__________, therefore they use the _____ system (Systeme Internationale d’Unites), International System.

• A defined unit in a system of measurement is called _______ unit.

• It is based on an object or event in the physical world.

reproduceSI

base

SI Base UnitsSI Base Units

Quantity Base Unit Abbreviation

Length

Time

Mass

Temperature

Amount of a substance

Luminous intensity

Electric current

meter m

second s

kilogram Kg

kelvin K

mole mol

candela cd

ampere A

Definitions of some derived Definitions of some derived unitsunits

• The __second___ is the frequency of microwave given of by a Cesium-13 atom.

• The ___meter ___ is the distance that light travels through __vacuum__ in 1/299,792,485 of a second.

• The __Kilogram___ is the mass of a platinum iridium cylinder metal stored in a triple bell jar, in Sevres, Paris.

• A __derived unit__ is a unit defined by a combination of base units . Examples : m/s, Km/h.

Derived unitsDerived units• The volume expressed in cm3 and dm3 is a

derived unit.

• 1 dm3 = __1__ L • 1 cm3 = __1_ mL• 1 L = _1,000 mL • 1 dm3 = _1,000 cm3

• A derived unit that relates the mass of an object per unit of volume is __density_.

Derived unitsDerived units

• The density of a substance is obtained dividing the _______ by the ________ of the object. Density can be measured in __g/cm3, g cm-3__ or __g/mL__

• Calculate the density of an object with a mass of 3.50g and which cause the water in a graduated cylinder to change from 12.5 mL to 18.7 mL.

mass volume

TemperatureTemperature

• The three scales for temperature are the ___Celsius___, __Fahrenheit and __Kelvin__.

• To change °C to °F the formula is:

__°F =__9/5°C + 32º

• To change °F to °C the formula is:

°C =_5/9(oF- 32o)

Examples:

Convert the following temperature to Fahrenheit

a) 25.0 oC b) 32.0 oC c) -7.8 oC

Convert the following temperature to Celsius

d) 70.0 oF e) 120.0 oF f) 50.0 oF

TemperatureTemperature

• To change °C to K the formula is:

K_=_oC + 273.16

• To change K to °C the formula is:

°C =__K – 273.16_

Examples:

Convert the following temperatures to K

a) 25.00 oC b) 32.43 oC c) -7.81 oC

Convert the following temperatures to Celsius

d) 300.00K e) 298.16K f) 79.38K

Complete Complete the following the following tabletable

Celsius Fahrenheit

Kelvin

Freezing point of water

Boiling point of water

Absolute zero 0

Room temperature

24

0

Conversion factorsConversion factors

• A conversion factor is a ratio of equivalent values used to express the same quantity in different units.

• A conversion factor is always equal to 1• Dimensional Analysis uses

__________________________.

•Look at the table of prefixes•Observe the values and the meanings•Complete the meanings

Practice:Express 2.45 x 10 2 hg in : a) g b) g and c) Eg

   

Solution a:Write the given with the unit :

2.45 x 10 2 hg

Multiply by a ratio

x

Write the unit that you want to cancel in the denominator

hg

Put the unit that you want to obtain in the numerator

g

Put the values to the fraction that will make numerator and denominator equivalent

1

10 8

Cancel out the equivalent units in the numerator and denominatorMultiply the quantity by the numerator and divide by the denominator

= 2.45 x 10 10 g

3.5 x 10 3 g x

CONVERSIONS

g

mg

1

10 3

= 3.5 x 10 6 mg

Express 3.5 x 10 3 g in : a) mg b) Pg and c) Kg

3.5 x 10 3 g x g

Pg1

10 15= 3.5 x 10 -12 Pg

3.5 x 10 3 g x g

Kg1

10 3

= 3.5 Kg

More practice: Express 1) 5.1 Kg in a) pg b) g c) Mg

2) 4.0 x 10 –7 Gm in a) Tm b) m c) am

3) 27 Kg in a) ng b) g c) Mg 4) 1.67 x 10 2 Gm in a) Tm b) m c) am

Number Digits to Count as Significant

Examples # of Significant

Digits

Nonzero digitsNonzero digits All 3,279

239

Leading zeroesLeading zeroes (zeroes before integer)

None 0.0045

0.00001

Captive zeroesCaptive zeroes (zeroes between two integers)

All 5.007205

Trailing zeroesTrailing zeroes (zeroes after the last integer)

Counted only if the number contains a decimal point

100

100.

100.0

0.0100

Scientific notation All in non-exponential part

1.7x10-7

1.30x1023

43

21

43

13

4

3 (1 and 0’s

following 1)

23

Uncertainty, accuracy and precisionThe last digit recorded in any measurement is anestimate and therefore it is UNCERTAIN.

6.526.536.54

The 6 and the 5 are certain.The red digits is uncertain. A measurement must be recordedwith all the certain digits and only one uncertain.

Let’s compareThe mass of an object measured in a simple balance was:

The mass of the same object measured in the analytical balance was:

2.359 are certain digits (you know them for sure). The last 6 is the estimate.

2.36g

The 2 and the 3 are certain digitsBut the 6 is uncertain.So you know for sure 2.3, but the following digit could be 5,6, 7 or even 4 or 9 because it is an estimate.

2.3596g

Which balance is more precise?

Accuracy: How close the number is to the accepted value.

Precision: How close the values are to each other. The smaller the uncertainty the greater the precision.

The accuracy of a measurement depends onthe calibration of the tool and also on how carfully the experimenter do the measurements.Well calibrated tools should give more accurate measurements if they are carefully done.

The precision depends on the tool. The analytical balance allows you to read more decimals and that is why it is more precise.

More precise tools should give more accurate values, but that is not always the case.

For example:The boiling point of water is 1000C(Accepted value)

Three thermometers were used to measure it experimentally.

100.00oC

100.oC

101.445oC

Classify each of them as accurate, precise or both

Random error: A measurement has equal possibilities of being high or low.

Systematic error: measurements are either all high or all low.

Example of Random error: In a certain experiment the values obtained for the boiling point of waterWere: 100.0oC , 99.8oC, 100.3oC, 100.2oC, 99.9oCHow do you solve it? Getting the average of the values

Example of systematic error: In another experiment the values obtained for the boiling point of water were: 100.2oC ,100.8oC, 100.3oC, 100.2oC, 100.9oC How do you solve it?

Calibrating the tool used to do the measurements

Significant figures or significant digits of a measurement are all the certain digits plus one and only one uncertain.

When multiplying and/or dividing :• Count the number of significant digits in each measurement.

Significant figures in calculations

•Report the answer with the same amount of significant digits as the measurement with the least amount of significant digits.

• Remember that exact numbers have infinite amount of significant figures.

3.802 x 2.0 =

Only 2 significant figuresAnswer: 7.6

4 significant figures2 significant figures

Count the decimals in each measurement.

Uncertainty in additions and subtractions

•Report the answer with the same amount of decimals as the measurement with the least amount of decimals.

• Remember the rules for rounding when doing your calculations.

Example. 2.038 + 2.1

3 decimals 1 decimal

2.038 + 2.1 = 4.1 (1 decimal)