Practice Quiz
Put the following in order from smallest to
largest.
 1.8x10-5
 8.7x1024
 0.7x10-3
 1.4x1040
Answers
Smallest
1.8x10-5 0.7x10-3
8.7x1024
Largest
1.4x1040
Scientists (and those studying
science) frequently must
deal with numbers that are
very large or very small.
Instead of wasting time by writing
many zeros before and after
numbers, a method of writing
very large and very small
numbers was invented. It is
called scientific notation.
Rules
1)
2)
3)
The first figure is a number
from 1 to 9.
The first figure is followed by a
decimal point and then the rest
of the figures.
Then multiply by the
appropriate power of 10.
Examples
 425=4.25x102
(102 is the same
as 100, so you are really
multiplying 4.25 by 100)
 0.00098=9.8x10-4 (10-4 is the
same as 1/1000, so you are
really multiplying 9.8 by 1/1000)
Practice
Write the following in scientific
notation:
36000
0.0135
Try These
Try to guess the answer without using
your calculator.
 4.2x104kg + 7.9x103kg=
 5.23x106mm x 7.1x10-2mm=
 5.44x107g/8.1x104mol=
 4.99x104kg
 3.7x105mm2
 6.72x102g/mol
Metric System
Metric System
Every measurement has two parts
 Number
 Scale (unit)
 SI system (le Systeme International)
based on the metric system
 Prefix + base unit
 Prefix tells you the power of 10 to
multiply by - decimal system -easy
conversions

The Fundamental SI Units
Copyright © Houghton Mifflin Company. All rights1–12
reserved.
Prefixes

giga-

mega - M
kilo  deci centi milli micro nano
G
k
d
c
m
m
n
1,000,000,000 109
1,000,000
106
103
0.1
10-1
0.01
10-2
0.001
10-3
0.000001
10-6
0.000000001 10-9
1,000
The Prefixes Used in the SI System
Copyright © Houghton Mifflin Company. All rights1–14
reserved.
Some
Examples
of
Commonly
Used Units
Copyright © Houghton Mifflin Company. All rights1–15
reserved.
Deriving the Liter
3
 Liter is defined as the volume of 1 dm
3
 gram is the mass of 1 cm
Measurement
of Volume
Copyright © Houghton Mifflin Company. All rights1–17
reserved.
Soda is Sold in 2-Liter Bottlesan Example of SI Units in
Everyday Life
Copyright © Houghton Mifflin Company. All rights1–18
reserved.
Figure 1.7 Common Types of Laboratory
Equipment Used to Measure Liquid Volume
Copyright © Houghton Mifflin Company. All rights1–19
reserved.
Measurement
of Volume
Using a Buret
Copyright © Houghton Mifflin Company. All rights1–20
reserved.
Mass and Weight
Mass is measure of resistance to
change in motion
 Weight is force of gravity.
 Sometimes used interchangeably
 Mass can’t change, weight can

Figure 1.8
An
Electronic
Analytic
Balance
Copyright © Houghton Mifflin Company. All rights1–22
reserved.
Significant Figures
Uncertainty
Basis for significant figures
 All measurements are uncertain to
some degree
 Precision- how repeatable
 Accuracy- how correct - closeness to
true value.
 Random error - equal chance of being
high or low- addressed by averaging
measurements - expected

Figure 1.10 The Results of Several Dart Throws
Show the Difference Between Precise and
Accurate
Neither accurate nor precise Precise but not accurate
(large random error)
(small random error,
large systematic error)
Copyright © Houghton Mifflin Company. All rights1–25
reserved.
Both precise and accurate
(small random error,
no systematic error)
Uncertainty
Systematic error- same direction each
time
 Want to avoid this
 Better precision implies better accuracy
 you can have precision without
accuracy
 You can’t have accuracy without
precision

Significant figures
Meaningful digits in a MEASUREMENT
 Exact numbers are counted, have
unlimited significant figures
 If it is measured or estimated, it has sig
figs.
 If not it is exact.
 All numbers except zero are significant.
 Some zeros are, some aren’t

Rules




All non zero digits are significant
Ex: 127
Zeros between significant digits are always significant
Ex: 106
Leading zeros are never significant
Ex: 0.005
Trailing zeros are significant only if there is a decimal
Ex: 25.30
Copy the examples below and write
the number of significant figures
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
7623142516
7084
0.00761
421.00
0.538
5000
5x103
5.0 x103
5000.
5120
Copy the examples below and write
the number of significant figures
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
7623142516 10
7084 4
0.00761 3
421.00 5
0.538 3
5000 1
5x103 1
5.0 x103 2
5000. 4
5120
3
Which zeroes count?
In between other sig figs does
 Before the first number doesn’t
 After the last number counts iff
 it is after the decimal point
 the decimal point is written in
 3200
2 sig figs


3200.
4 sig figs
Multiplication and Division
The final answer should have the same
number of sig figs as the measurement
having the smallest number of sig figs
Ex: 10.305g x 0.00320g=

Ex: 3.64928g/5.2mL=
Addition and Subtraction

Line the numbers up in column form
Ex: 3.461728+14.91+0.98001+5.2631=
Ex: 467.384-2.384=
Ex: 564321-264321=
Doing the math
Multiplication and division, same
number of sig figs in answer as the
least in the problem
 Addition and subtraction, same number
of decimal places in answer as least in
problem.

Rounding Numbers
Copyright © Houghton Mifflin Company. All rights1–35
reserved.
Significant Figures Song
To the tune of Three Blind Mice
Verse 1
Addition and Subtraction line numbers
up in columns (Repeat)
 Make sure the decimals are aligned
right,
Take off the numbers that are on the
right
 To get the sig figs (Repeat)

Verse 2
Multiplication and division count the
numbers (Repeat)
 Find the one that is the least
That’s the number, the rest will cease
 To get the sig figs (Repeat)

Temperature
Temperature
A measure of the average kinetic
energy
 Different temperature scales, all are
talking about the same height of
mercury.
 Derive a equation for converting ºF toºC

0ºC = 32ºF
0ºC
32ºF
(0,32)= (C1,F1)
ºF
ºC
100ºC = 212ºF
0ºC = 32ºF
0ºC 100ºC
212ºF 32ºF
(0,32) = (C1,F1)
(120,212) = (C2,F2)
ºF
ºC
100ºC = 212ºF
0ºC = 32ºF
100ºC = 180ºF
0ºC 100ºC
212ºF 32ºF
100ºC = 212ºF
0ºC = 32ºF
100ºC = 180ºF
1ºC = (180/100)ºF
1ºC = 9/5ºF
0ºC 100ºC
212ºF 32ºF
Figure 1.11 The Three Major
Temperature Scales
Copyright © Houghton Mifflin Company. All rights1–47
reserved.
Figure 1.12 Normal Body
Temperature
Copyright © Houghton Mifflin Company. All rights1–48
reserved.
Equations
F=1.80(C)+32
C=(F-32)/1.80
Dimensional Analysis
Using the units to solve problems
Dimensional Analysis
Use conversion factors to change the units
 Conversion factors = 1
 1 foot = 12 inches (equivalence statement)
 12 in = 1 = 1 ft.
1 ft.
12 in
 2 conversion factors
 multiply by the one that will give you the
correct units in your answer.

Examples #1,2
11 yards = 2 rod
 40 rods = 1 furlong
 8 furlongs = 1 mile
 The Kentucky Derby race is 1.25 miles.
How long is the race in rods, furlongs,
meters, and kilometers?
 A marathon race is 26 miles, 385 yards.
What is this distance in rods, furlongs,
meters, and kilometers?

Example #3
Science fiction often uses nautical
analogies to describe space travel. If the
starship U.S.S. Enterprise is traveling at
warp factor 1.71, what is its speed in
knots?
 Warp 1.71 = 5.00 times the speed of light
 speed of light = 3.00 x 108 m/s
 1 knot = 2000 yd/h exactly

Example #4
Apothecaries (druggists) use the
following set of measures in the English
system:
 20 grains ap = 1 scruple (exact)
 3 scruples = 1 dram ap (exact)
 8 dram ap = 1 oz. ap (exact)
 1 dram ap = 3.888 g
 1 oz. ap = ? oz. troy
 What is the mass of 1 scruple in grams?

Example #5

The speed of light is 3.00 x 108 m/s.
How far will a beam of light travel in
1.00 ns?
Group Practice
Group Practice-no flashcards
1) Convert 0.049kg of sulfur to grams.
2) Convert 3µL of saline solution to liters.
3) Convert 150mg of aspirin to grams.
4) Convert 1.18dm3 to mL.
5) Convert 5230000nL of water to grams.
6) Convert 4.19L to cubic centimeters
7) Convert 310000cm3 of concrete to
cubic meters
Complex Conversion
Problems
#1
A heater gives off heat at a
rate of 330kJ/min. What is
the rate of heat output in
kilocalories per hour? (1
cal=4.184J)
#1 Answer
3
4.7x10
kcal/h
#3
At the equator, Earth rotates
with a velocity of about 465
m/s. What is the velocity in
kilometers per hour? What is
the velocity in kilometers per
day?
#3 Answer
1670km/hr
4
4.02x10 km/d
#2
A water tank leaks water at
the rate of 3.9mL/h. If the
tank is not repaired, what
volume of water in liters
will it leak in a year?
#2 Answer
34L/yr
Density
Density
Ratio of mass to volume
 D = m/V
 Useful for identifying a compound
 Useful for predicting weight
 An intrinsic property- does not depend
on what the material is

Formula
Density=Mass/Volume
 D=m/V
 If you know the density triangle, you can
get the formulas for m and V.
 The units of density are always going to
have a division sign in them. Ex: g/mL

Densities of Various Common
Substances* at 20° C
Copyright © Houghton Mifflin Company. All rights1–68
reserved.
Example #1

An empty container weighs 121.3 g. Filled
with carbon tetrachloride (density 1.53
g/cm3 ) the container weighs 283.2 g.
What is the volume of the container?
Example #2

A 55.0 gal drum weighs 75.0 lbs. when
empty. What will the total mass be when
filled with ethanol?
density 0.789 g/cm3
1 gal = 3.78 L
1 lb = 454 g
Examples #3, 4, and 5
(on your own)
3) Mercury has a density of 13.6g/mL.
What volume of mercury must be taken
to obtain 225g of the metal?
4) Isopropyl alcohol has a density of
0.785g/mL. What volume should be
measured to obtain 20.0g of the liquid?
5) A beaker contains 725mL of water. The
density of water is 1.00g/mL. Calculate
the volume and mass of the water.
Answers
3) 16.5mL
4) 31.8mL
5) 0.725L, 0.725g