Copyright © Houghton Mifflin Company. All rights reserved.2–12–1 2.1 Measurement Systems...

Copyright © Houghton Mifflin Company. All rights reserved. 2–1

2.1 Measurement Systems

Measurement is the determination of the dimensions, capacity,

quantity, or extent of something.


2.1 Measurements in Chemistry

always consists of two partsNUMBER

EXACT or INEXACT

SIGNIFICANT FIGURES

SCIENTIFIC NOTATION

UNIT

METRIC SYSTEM

DIMENSIONAL ANALYSIS


2.1 Metric System UnitsSystem Internationale (SI)

Mass kilogram (kg), gram (g)Lengthmeter (m), centimeter (cm)Volume cubic meter (m3),

cubic centimeter (cm3)liter (L) = 1000 cm3 (exact)milliliter (mL) = 1 cm3 (exact)

Time second (s)Temperature kelvin (k)

Celsius (ºC)


Common Metric System Prefixes with Their Symbols and Mathematical Meanings.

Numerical prefixes for larger or smaller units:

mega (M)1000000 times unit (106)

kilo (k) 1000 times unit (103)

deci (d) 0.01 times unit (10-1)

centi (c) 0.01 times unit (10-2)

milli (m) 0.001 times unit (10-3)

micro (µ)0.000001 times unit (10-6)

My King Died Chewing M & M’s

Memorize these!


Figure 2.2 Comparisons of the base metric system units of length (meter), mass (gram), and volume (liter) with common objects.


Derived Units in the Metric System.

Frequency (cycles/s, hertz)

Density (mass/volume, g/cm3)

Speed (distance/time, m/s)

Acceleration (distance/(time)2, m/s2)

Force (mass x acceleration, kg•m/s2, newton)

Pressure (force/area, kg/(m•s2), pascal)

Energy (force x distance, kg•m2/s2, joule)


2.3 Exact and Inexact Numbers

Exact Numbers

Have no uncertainty associated with them

From measurement of indivisible objects

10 tennis balls

29 students enrolled

Some conversion factors

Exactly 2.54 centimeters = one inch


2.3 Exact and Inexact Numbers

Inexact Numbers

Have some uncertainty associated with them

From scalar measurements

“Stuff” rather than “Things”

Values are limited by the instrument

14.3 gallons ( 6 oz)

14.325 gallons ( 1 tsp)


2.4 Uncertainty in Measurement and Significant Figures

Significant figures (sig figs or sig digs) are the digits in an inexact number.

The last digit in an inexact number is an estimated value.

The number of sig figs depends upon the instrument used.

14.3 gallons 14.325 gallons


2.4 Uncertainty in Measurement and Significant Figures

Exact numbers have an infinite number of significant figures. They do not contain an estimated value.

10 tennis balls

2.54 cm = 1 inch


2.5 Significant Figures and Mathematical Operations

When is zero a significant figure?

Trailing zeros are always sig. figs.11.0 ____ sig. figs.

100 ____ sig. figs.

Trailing zeros are significant because they are the best estimate of the value.

10.9 11.0 (best estimate) 11.1



When is zero a significant figure?

Embedded zeros are always sig. figs.101 ____ sig. figs.

10.11 ____ sig. figs.

Leading zeros are never sig. figs.0.00145 ____ sig. figs.

0.0000000000234 ____ sig. figs.


Chemistry at a Glance:Significant Figures



Multiplication and DivisionThe result can have no more sig. figs.

than the fewest number of sig. figs. used to obtain the result.

4.242 x 1.23 = 5.21766 5.22

12.24 / 2.0 = 6.12 6.1


2.5 Significant Figures and Mathematical OperationsAddition and Subtraction

Result will have a digit as far to the right as all the numbers have a digit in common

2.02 8.7397 1.234 -2.123+ 3.6923 6.6167 6.9463

6.95 6.617



Rounding Off

When the last sig. fig. is followed by a number equal to or greater than 5, round the last sig. fig. up.

When the last sig. fig. is followed by a number less than 5, leave the last sig. fig. as is.


2.6 Scientific Notation

Used for very large or very small numbers

Distance from earth to sun

93,000,000 miles

Diameter of a carbon atom

0.000000000015 meters



An ordinary decimal number is expressed as the product of a coefficient between 1 and 10, and an exponential term.

Express in scientific notation:

93,000,000 miles

0.000000000015 meters



Scientific notation is useful for handling significant figures.

Give the result to the proper number of significant figures:

(25.456 – 25.423) x 64.58 x 430 =

0.01553 45.0 =


2.7 Conversion Factors and Dimensional Analysis

A conversion factor is a ratio that specifies how one unit of measurement is related to another:

1 inch = 2.54 cm

_1 in__ 2.54 cm2.54 cm 1 in



Dimensional analysis is a problem-solving method in which the units of the meas-urement are used to set up the calcula-tion.

Units behave like numbers, they can be multiplied, divided, or cancelled.



What is the volume of a cube if its edges are 2.5 cm long?

How long is a foot in centimeters?

Convert 0.0256 mm to m.



How many miles will I travel in 3.00 hours at 65.0 miles per hour?

How long will it take to travel 500 miles at 65 miles per hour?

What is my speed, in miles per hour, if I ride my bike 25.5 miles in 1.20 hours?


2.8 DensityMatter has mass and volume.

Density is the ratio of mass to volume for a specific type of matter.

Density = _mass_ _grams_ volume milliliters

Density is a characteristic property of a pure substance.


Left: Shortening floats on water.

Right: Copper floats on mercury


Liquids that do not dissolve in one another and that have different densities float on one another, forming layers.


Table 2.3 Densities of Selected Substances


2.8 Density

Water has a density of 1.00 g/mL at 20°C. What is the mass of 20.0 mL of water?

20.0 mL of gasoline has a mass of 11.2 g. What is its density?

What volume of ethyl alcohol will have a mass of 20.0 g? Its density is 0.79 g/mL.


2.9 Temperature Scale and Heat Energy

Heat is a form of energy. Temperature can be used to measure heat.

1 calorie = amount of heat required to raise temperature of 1 gram of water by 1 Celcius

1 Calorie = 1000 calories = 1 kcal

1 Calorie = 4.184 Joule


The relationships among the Celsius, Kelvin, and Fahrenheit temperature scales are determined by the

degree sizes and the reference point values.

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