1. What is measurement? Units of Measurement When do you Measure?
measure your height.
read your watch.
take your temperature.
weigh a cantaloupe.

2. Measurement in Chemistry
In chemistry we
measure quantities.
do experiments.
calculate results.
use numbers to report measurements.
compare results to standards.
all with needed tools
every measurement,
number followed by unit
Number and Unit
35 m
0.25 L
225 lb
3.4 hr

3. The Metric System (SI) metric system or SI (international system)
decimal system based on 10.
Used worldwide.(M)
Used by scientists (SI).
following unit used for each type of measurement: Measurement Metric SI Length meter (m) meter (m) Volume liter (L) cubic meter (m3) Mass gram (g) kilogram (kg) Time second (s) second (s) Temperature Celsius (C) Kelvin (K)

4. Length Measurement Length measured using a meter stick.
Uses unit of meter (m) in both systems.
unit of an inch equal to exactly 2.54 centimeters in metric (SI) system.
1 in. = 2.54 cm

5. Volume Measurement Volume space occupied by a substance.
measured using a graduated cylinder (liquids)
metric system
unit liter (L) in
1 L = qt
SI system (solids)
m3(cubic meter)

6. Mass Measurement mass of an object quantity of material it contains.
measured
balance.
metric system
. gram (g)
SI system
kilogram (kg)
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7. Temperature Measurement
temperature of a substance
indicates how hot or cold.
metric system
Celsius (C)
SI system
Kelvin (K) scale.
thermometer here shows
18ºC or 64ºF.

8. Time Measurement Time measurement metric and SI systems.
second(s)
based on an atomic clock
uses a frequency emitted by cesium atoms

9. What are scientific notation?
very large or very small numbers
coefficient and a power of 10
width human hair is m
written 8 x 10-6 m.
large number such as s
written 4.5 x 106 s
Let’s explore more !
coefficient power of ten coefficient power of ten
x x
decimal point moved after first digit
spaces moved shown as power of ten.
= x = x 10-3
4 spaces left spaces right

10. Numbers written in standard format
Some Powers of Ten
Numbers written in standard format
and in scientific notation.
Diameter of the Earth m
1.28 x 107 m
Mass of a human
68 kg
6.8 x 101 kg
Length of a pox virus cm
3 x 10-5 cm

11. What are measured numbers ?
. l l l l l cm
determine a quantity such as height or mass
markings on meter stick end of orange line are read as
first digit
plus second digit
last digit obtained by estimating
length reported as 2.76 cmdigits 2 and 7 are certain (known).
The final digit 6 was estimated (uncertain).
All three digits (2.76) are significant including estimated digit.

12. Zero as a Measured Number!
. l l l l l5. . cm
For this measurement
first and second known digits are 4.5.
line ends on mark
estimated digit in hundredths place 0.
measurement
reported as 4.50 cm.

13. What are significant numbers?
Significant figures
obtained from
measurement
include all known
digits plus estimated digit.
reported
measurement depend on measuring tool.
non-zero numbers in measured number are significant.
38.15 cm ft 2
65.6 lb
m 5

14. The two kinds of zeros? Trailing zeros & Leading zeros
follow non-zero numbers in numbers without decimal points.
Precede non-zero digits in a decimal number
are usually place holders.
are not significant.
Number significant digits cm
200 kg
oz 3
lb 2
g 5
Sandwiched zeros
occur between nonzero numbers.
are significant.
Number significant digits
50.8 mm 3
2001 min lb 3
m 5

15. What are prefixes? front of a unit increases or decreases size
A prefix
front of a unit increases or decreases size
makes units larger or smaller
one or more factors of 10.
indicates a numerical value.
prefix = value
1 kilometer = meters
1 kilogram = grams

16. Metric and SI Prefixes need to know!

17. What are metric equalities?
An equality
states same measurement in two different units.
can be written using
relationships between two metric units.
Example: 1 meter same as 100 cm and 1000 mm.
1 m = cm
1 m = mm

18. Measuring Length 1 km = 1000 m 1 m = 1000 mm 1 m = 100 cm
Several equalities can
be written for length
metric (SI) system
1 km = m
1 m = mm
1 m = cm
1 mm = m

19. Measuring Volume Several equalities can be written for volume metric
(SI) system
1 kl = l
1 l = ml
1 l = cl
1 ml = l

20. Measuring Mass Several equalities can be written for mass
metric (SI) system
1 kg = g
1 g = mg
1 g = cg
1 mg = g

21. Other equalities between metric and U.S. units?
use two different units
Describe same measured amount.
written for relationships between units of the metric system, U.S. units, or between
For example,
1 m = mm
1 lb = oz
2.205 lb = 1 kg

22. Some Common Equalities
contents of packaged foods
U.S. are listed as both metric and U.S. units
Indicate same amount of a substance in two different units.

23. Use conversion factors to change between units!
A conversion factor
fraction obtained from an equality
Equality: 1 in. = 2.54 cm
written as a ratio with a numerator and denominator.
can be inverted to give two conversion factors for every equality.
1 in and cm
2.54 cm 1 in.

24. Conversion Factors in a Problem
A conversion factor
may be obtained from information in a word problem.
written for that problem only.
Example 1:
The price of one pound (1 lb) of red peppers is $2.39.
1 lb red peppers and $2.39
$ lb red peppers
Example 2:
The cost of one gallon (1 gal) of gas is $2.34.
1 gallon of gas and $2.34
$ gallon of gas

25. Percent as a Conversion Factor
A percent factor
Gives ratio of the parts to whole.
% = Parts x 100
Whole
Uses same unit to express percent.
Uses value 100 and unit for whole.
can be written as two factors.
Example: A food contains 30% (by mass) fat.
30 g fat and 100 g food
100 g food 30 g fat

26. Another example! The thickness of the skin fold at
the waist indicates 11% body
fat. What percent factors can be
written for body fat in kg?
Percent factors using kg:
11 kg fat and 100 kg mass
100 kg mass 11 kg fat

27. Given and Needed Units can be used in problem solving!
To solve a problem
Identify given unit
Identify needed unit.
Example:
A person has a height of 2.0 meters.
What is that height in inches?
given unit is initial unit of height.
given unit = meters (m)
needed unit is unit for answer.
needed unit = inches (in.)

28. Learning Check An injured person loses 0.30 pints of blood. How
many milliliters of blood would that be?
Identify the given and needed units given in this
problem.
Given unit = _______
Needed unit = _______

29. Problem Setup steps! Write given and needed units.
Write a unit plan to convert given unit to needed unit.
Write equalities and conversion factors to connect units.
Use conversion factors to cancel given unit and provide needed unit.
Unit x Unit = Unit 2
Unit 1
Given x Conversion = Needed
unit factor unit

30. Setting up a Problem How many minutes are 2.5 hours?
Given unit = hr
Needed unit = min
Unit Plan = hr min
Setup problem to cancel hours (hr).
Given Conversion Needed
unit factor unit
2.5 hr x 60 min = 150 min (2 SF)
1 hr
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Publishing as Benjamin Cummings

31. A solved example
A rattlesnake is 2.44 m long. How many centimeters long is the snake?
Given Conversion Needed
unit factor unit
2.44 m x cm = 244 cm
1 m

32. Using Two or More Factors
Often, two or more conversion factors are required to obtain unit needed for answer.
Unit 1 Unit 2 Unit 3
Additional conversion factors are placed in setup to cancel each preceding unit
Given unit x factor 1 x factor 2 = needed unit
Unit x Unit x Unit = Unit 3
Unit Unit 2

33. Example: Problem Solving
How many minutes are in 1.4 days?
Given unit: 1.4 days
Factor Factor 2
Plan: days hr min
Set up problem:
1.4 days x 24 hr x 60 min = 2.0 x 103 min
1 day hr
2 SF Exact Exact = 2 SF

34. Remember to check the unit cancellation!
check your unit cancellation in setup.
units in conversion factors must cancel to give correct unit for answer.
What is wrong with the following setup?
1.4 day x 1 day x hr
24 hr min
Units = day2/min is not the unit needed
Units don’t cancel properly.

35. Another example! the GPS
What is 165 lb in kg?
STEP 1 Given 165 lb Need kg
STEP 2 Plan
STEP 3 Equalities/Factors
1 kg = 2.20 lb
2.20 lb and kg
1 kg lb
STEP 4 Set Up Problem
165 lb x kg = kg
2.20 lb

36. A bucket contains 4.65 L of water. How many gallons of water is that?
Given: L Needed: gallons
Plan: L qt gallon
Equalities: 1.06 qt = 1 L; 1 gal = 4 qt
Set Up Problem:
4.65 L x x qt x 1 gal = gal
1 L qt
3 SF SF exact SF

37. If a ski pole is 3.0 feet in length, how long is the ski pole in mm?
3.0 ft x 12 in x cm x 10 mm =
1 ft in cm
Calculator answer: mm
Needed answer: mm (2 SF rounded)
Check factor setup: Units cancel properly
Check needed unit: mm

38. If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7500 feet?
Given: ft 65 m/min Need: min
Plan: ft in cm m min
Equalities: 1 ft = 12 in in. = 2.54 cm 1 m = 100 cm
1 min = 65 m (walking pace)
Set Up Problem:
7500 ft x in. x cm x 1m x 1 min
1 ft in cm m
= 35 min final answer (2 SF)

39. Percent Factor in a Problem
If the thickness of the skin fold at the waist indicates an 11% body fat, how much fat is in a person with a mass of 86 kg?
percent factor
86 kg mass x kg fat
100 kg mass
= 9.5 kg fat
Copyright © by Pearson Education, Inc.
Publishing as Benjamin Cummings

40. Another example:
How many lb of sugar are in 120 g of candy if the candy is 25%(by mass) sugar?
percent factor
120 g candy x 1 lb candy x 25 lb sugar
454 g candy lb candy
= lb sugar

41. What is density? Density Compares the mass of an object to its volume.
Is the mass of a substance divided by its volume.
Density expression
Density = mass = g or g = g/cm3
volume mL cm3
Note: 1 mL = 1 cm3
Ice floats in water
because density of ice is less than density of water.
Aluminum sinks
because its density is greater than density of water

42. Problem on density
Osmium is a very dense metal. What is its density in g/cm3 if 50.0 g of osmium has a volume of 2.22 cm3?
Given: mass = 50.0 g volume = 22.2 cm3
Plan: Place the mass and volume of the osmium metal
in the density expression.
D = mass = g
volume cm3
calculator = g/cm3
final answer (2) = g/cm3

43. How to determine volume by displacement ?
solid completely submerged in water displaces its own volume of water.
volume of solid is calculated from volume difference.
45.0 mL mL
= 9.5 mL = 9.5 cm3

44. Density Using Volume Displacement
The density of the zinc object is
then calculated from its mass
and volume.
mass = g = 7.2 g/cm3 volume cm3

45. Find the volume first?
What is the density (g/cm3) of 48.0 g of a metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added?
33.0 mL
25.0 mL
object

46. Solution Given: 48.0 g Volume of water = 25.0 mL
Volume of water + metal = 33.0 mL
Need: Density (g/mL)
Plan: Calculate the volume difference. Change to cm3,
and place in density expression.
33.0 mL mL = mL
8.0 mL x 1 cm3 = cm3
1 mL
Set up Problem:
Density = g = g = 6.0 g/cm3
8.0 cm cm3