1 Chapter 2 Measurements 2.1 Units of Measurement Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
May 21, 2015
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Chapter 2 Measurements
2.1
Units of Measurement
Copyright © 2008 by Pearson Education, Inc.Publishing as Benjamin Cummings
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Measurement
You make a measurement
every time you• Measure your height. • Read your watch.• Take your temperature.• Weigh a cantaloupe.
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Measurement
In a measurement
• A measuring tool is used to compare some dimension of an object to a standard.
• Of the thickness of the skin fold at the waist, calipers are used.
Copyright © 2008 by Pearson Education, Inc.Publishing as Benjamin Cummings
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Stating a Measurement
In a measurement, a number is followed by a unit.
Observe the following examples of measurements:
Number Unit
35 m
0.25 L
225 kg
3.4 hr
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The Metric System (SI)
The metric system or SI (international system) is
• A decimal system based on 10.
• Used in most of the world.
• Used everywhere by scientists.
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Units in the Metric System
In the metric (SI) system, one unit is 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)
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For each of the following, indicate whether the unit describes 1) length, 2) mass, or 3) volume.
____ A. A bag of onions has a mass of 2.6 kg.
____ B. A person is 2.0 m tall.
____ C. A medication contains 0.50 g aspirin.
____ D. A bottle contains 1.5 L of water.
Learning Check
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For each of the following, indicate whether the unit describes 1) length, 2) mass, or 3) volume.
2 A. A bag of onions has a mass of 2.6 kg.
1 B. A person is 2.0 m tall.
2 C. A medication contains 0.50 g aspirin.
3 D. A bottle contains 1.5 L of water.
Solution
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Learning Check Identify the measurement with an SI unit. A. John’s height is
1) 1.5 yd 2) 6 ft 3) 2.1 m
B. The race was won in1) 19.6 s 2) 14.2 min 3) 3.5 hr
C. The mass of a lemon is1) 12 oz 2) 0.145 kg 3) 0.6 lb
D. The temperature is1) 85C 2) 255 K 3) 45F
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Solution Identify the measurement with an SI unit. A. John’s height is
3) 2.1 m
B. The race was won in1) 19.6 s
C. The mass of a lemon is2) 0.145 kg
D. The temperature is2) 255 K
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STEP 1 State the given and needed units.
STEP 2 Write a plan to convert the given unit to the
needed unit.
STEP 3 Write equalities/conversion factors that connect the units.
STEP 4 Set up problem with factors to cancel
units and calculate the answer.
Unit 1 x Unit 2 = Unit 2Unit 1
Given Conversion Needed unit factor unit
Guide to Problem Solving (GPS)
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Setting up a Problem
How many minutes are 2.5 hours?
given unit = 2.5 hr
needed unit = ? min
plan = hr min
Set up problem to cancel units (hr).
given conversion needed unit factor unit
2.5 hr x 60 min = 150 min
1 hr
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A rattlesnake is 2.44 m long. How long is the snake
in centimeters?
1) 2440 cm
2) 244 cm
3) 24.4 cm
Learning Check
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A rattlesnake is 2.44 m long. How long is thesnake in centimeters?
2) 244 cm
given conversion needed unit factor unit
2.44 m x 100 cm = 244 cm 1 m
Solution
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• Often, two or more conversion factors are required to obtain the unit needed for the answer.
Unit 1 Unit 2 Unit 3
• Additional conversion factors can be placed in the setup to cancel each preceding unitGiven unit x factor 1 x factor 2 = needed unitUnit 1 x Unit 2 x Unit 3 = Unit 3
Unit 1 Unit 2
Using Two or More Factors
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How many minutes are in 1.4 days?
Given unit: 1.4 days Needed unit: min
Plan: days hr min
Equalties: 1 day = 24 hr
1 hr = 60 min Set up problem: 1.4 days x 24 hr x 60 min = 2.0 x 103
min
1 day 1 hr
Example: Problem Solving
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• Be sure to check your unit cancellation in the setup.
• The units in the conversion factors must cancel to give the correct unit for the answer.
What is wrong with the following setup?1.4 day x 1 day x 1 hr
24 hr 60 min
Units = day2/min is Not the needed unit
Units don’t cancel properly.
Check the Unit Cancellation
More units
Area m2 = m x m Volume m3 = m x m x m Density mass/volume
g/mL or Kg/L
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K = oC + 273 Ex 23 oC = _______ K 135 K = ________ oC
1L = 1 dm3
1 m3 =1000L
Ex 27 m3 = ________ L23
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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?
1) 2.25 g/cm3
2) 22.5 g/cm3
3) 111 g/cm3
Learning Check
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Given: mass = 50.0 g volume = 2.22 cm3
Plan: Write the density expression.
D = mass volume
Express mass in grams and volume in cm3
mass = 50.0 g volume = 2.22 cm3
Set up problem using mass and volume.D = 50.0 g = 22.522522 g/cm3
2.22 cm3
= 22.5 g/cm3
Solution
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Volume by Displacement
• A solid completely submerged in water displaces its own volume of water.
• The volume of the solid is calculated from the volume difference.45.0 mL - 35.5 mL
= 9.5 mL = 9.5 cm3
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Density Using Volume Displacement
The density of the object iscalculated from its mass andvolume. mass = 68.60 g = 7.2 g/cm3
volume 9.5 cm3
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Sink or Float
• Ice floats in water because the density of ice is less than the density of water.
• Aluminum sinks because its density is greater than the density of water.
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Which diagram correctly represents the liquid layers in the cylinder? Karo (K) syrup (1.4 g/mL), vegetable (V) oil (0.91 g/mL,) water (W) (1.0 g/mL)
1 2 3
K
K
W
W
W
V
V
V
K
Learning Check
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1)
vegetable oil 0.91 g/mL
water 1.0 g/mL
Karo syrup 1.4 g/mL
K
W
V
Solution
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Chapter 2 Measurements
2.2
Scientific Notation
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Scientific NotationScientific notation • Is used to write very large
or very small numbers.• For the width of a human
hair of 0.000 008 m is written as
8 x 10-6 m• For a large number such
as 2 500 000 s is written as
2.5 x 106 s Copyright © 2008 by Pearson Education, Inc.Publishing as Benjamin Cummings
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Scientific Notation
• A number written in scientific notation contains a coefficient and a power of 10.
coefficient power of ten coefficient power of ten
1.5 x 102 7.35 x 10-4
• To write a number in scientific notation, the decimal point is moved after the first digit.
• The spaces moved are shown as a power of ten.
52 000. = 5.2 x 104 0.00378 = 3.78 x 10-
3
4 spaces left 3 spaces right
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Some Powers of Ten
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Comparing Numbers in Standard and Scientific Notation
Number in Standard Format Scientific NotationDiameter of the Earth 12 800 000 m 1.28 x 107 mMass of a human 68 kg 6.8 x 101 kgMass of a hummingbird 0.002 kg 2 x 10-3 kg Length of a pox virus 0.000 000 3 cm 3 x 10-7 cm
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Learning Check
Select the correct scientific notation for each.
A. 0.000 008
1) 8 x 106 2) 8 x 10-6 3) 0.8 x 10-5
B. 72 000
1) 7.2 x 104 2) 72 x 103 3) 7.2 x 10-4
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Solution
Select the correct scientific notation for each.
A. 0.000 008
2) 8 x 10-6
B. 72 000
1) 7.2 x 104
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Learning Check
Write each as a standard number.
A. 2.0 x 10-2
1) 200 2) 0.0020 3) 0.020
B. 1.8 x 105
1) 180 000 2) 0.000 018 3) 18 000
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Solution
Write each as a standard number.
A. 2.0 x 10-2
3) 0.020
B. 1.8 x 105
1) 180 000