Chapter 2 Measurements and Calculations. Copyright © Houghton Mifflin Company. All rights...

Chapter 2

Measurements and

Calculations

Copyright © Houghton Mifflin Company. All rights reserved. 2 | 2

Scientific Notation

• Technique used to express very large or very small numbers: for example, 2,009,345,234 or 0.00000045723

• Expressed as a product of a number between 1 and 10 and a power of 10


Writing Numbersin Scientific Notation

1 Locate the decimal point.2 Count the number of places the decimal point must

be moved to obtain a number between 1 and 10.3 Multiply the new number by 10n where n is the

number of places you moved the decimal point.4 Determine the sign on the exponent n.

– If the decimal point was moved left, n is +

– If the decimal point was moved right, n is –

– If the decimal point was not moved, n is 0


Write the following numbers in scientific notation:

A. 2,009,345,234

B. 0.00000045723


Converting from Scientific Notation to Standard Form

1 Determine the sign of n in 10n

– If n is + the decimal point will move to the right.

– If n is – the decimal point will move to the left.

2 Determine the value of the exponent of 10.– Tells the number of places to move the

decimal point

3 Move the decimal point and rewrite the number.


Convert from Scientific Notation to Standard Form:

2.0684 x 105

3.28409 x 10-4


Related Units in the Metric System

• All units in the metric system are related to the fundamental unit by a power of 10.

• A power of 10 is indicated by a prefix.• Prefixes are always the same, regardless of

the fundamental unit.• Examples:

kilogram = 1000 gramskilometer = 1000 meters


Some Fundamental SI Units


Prefixes

• All units in the metric system utilize the same prefixes


Length


Volume

• Measure of the amount of 3-D space occupied by a substance

• SI unit = cubic meter (m3)• Commonly measure solid

volume in cubic centimeters (cm3)

• 1 mL = 1 cm3


Mass

• Measure of the amount of matter present in an object

• SI unit = kilogram (kg)

1 kg = 2.205 pounds, 1 lb = 453.59 g

68 kg = 150 lbs

• Commonly measure mass in grams (g) or milligrams (mg)


Uncertainty in Measured Numbers

• A measurement always has some amount of uncertainty.

• To understand how reliable a measurement is, we must understand the limitations of the measurement.

• Example:


Reporting Measurements

• Significant figures: system used by scientists to indicate the uncertainty of a single measurement

• Last digit written in a measurement is the number that is considered uncertain

• Unless stated otherwise, uncertainty in the last digit is ±1.


Rules for Counting Significant Figures

• Nonzero integers are always significant.example: 4.675 = 4 sig figs

• Zeros – Leading zeros never count as significant figures.

example: 0.000748 = 3 sig figs

– Captive zeros are always significant.example: 2.0087 = 5 sig figs

– Trailing zeros are significant if the number has a decimal point.

example: 6.980 = 4 sig figs


Exact Numbers

• Exact numbers: numbers known with certainty – Counting numbers

• number of sides on a square

– Defined numbers• 100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm

• 1 minute = 60 seconds

• Have unlimited number of significant figures


Rules for Rounding Off

• If the digit to be removed:– is less than 5, the preceding digit stays the same.

example:

– is equal to or greater than 5, the preceding digit is increased by 1.

example: In a series of calculations, carry the extra digits to the final result,

then round off.

example:

• When rounding off use only the first number to the right of the last significant figure.

example:


Round these numbers to four significant figures:

• 157.387

• 443,678

• 80, 332

• 7.8097


Multiplication/Division withSignificant Figures

• Result must have the same number of significant figures as the measurement with the smallest number of significant figures:

example: 3.5 x 3.5609 =

example: 4.98/11.76 =


Adding/SubtractingNumbers with Significant Figures

• Result is limited by the number with the smallest number of significant decimal places

example:


Problem Solvingand Dimensional Analysis

• Many problems in chemistry involve using equivalence statements to convert one unit of measurement to another.

• Conversion factors are generated from equivalence statements.– e.g. 1 mi = 5,280. ft can give:

1 mi/5280. ft or

5280. ft/1 mi


Converting One Unit to Another

• Find the relationship(s) between starting and goal units. Write equivalence statement for each relationship.

Given quantity x unit factor = desired quantity

• Write a conversion factor for each equivalence statement.

• Arrange the conversion factor(s) to cancel with starting unit and result in goal unit.


Converting One Unit to Another (cont.)

• Check that units cancel properly.

• Multiply and divide the numbers to give the answer with the proper unit.

• Check significant figures.

• Check that your answer makes sense!


Convert the following: (Use Table 2.7)

• 180 lbs to kg

• 12.3 mi to in.


Temperature Scales


Some facts concerning the temperature scales:

• The size of each degree is the same for the Celsius and Kelvin scales.

• The Fahrenheit degree is smaller than the Celsius and Kelvin unit.

F – 180 degrees between freezing and boiling point of water

C – 100 degrees between freezing and boiling point of water

• All three scales have different zero points.


Converting between Kelvin and Celsius ScalesToC + 273 = K

• Celsius to Kelvin: add 273 to C temperatureexample: Convert 46o C to K

• Kelvin to Celsius: subtract 273 from K temperature

example: Convert 4 K to C


Converting from Celsius to Fahrenheit

• Requires two adjustments:

1. Different size units; 180 F degrees = 100 C degrees

2. Different zero points

ToF = 1.80(ToC) + 32

Convert 30oC to oF


Converting from Fahrenheit to Celsius

ToC = (ToF – 32)/1.80

Convert 102oF to oC


Density

• Volume of a solid can be determined by water displacement.

Volume

MassDensity


Using Density in Calculations

Volume

MassDensity

Density

Mass Volume

Volume Density Mass


Using Density in Calculations

• Calculate the density of an object which weighs 35.7 g and occupies a volume of 21.5 mL.

• Calculate the mass of a piece of copper which occupies

2.86 cm3. (density = 8.96 g/cm3)

• Calculate the volume of an object with a density of 4.78 g/mL

and mass of 20.6 grams.

Date post:	19-Dec-2015
Category:	Documents
View:	219 times
Download:	2 times

Chapter 2 Measurements and Calculations. Copyright © Houghton Mifflin Company. All rights...

Documents