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Standards for Measurement Standards for Measurement

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Mass and WeightMass and Weight

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•Matter: Anything that has mass and occupies space.

•Mass : The quantity or amount of matter that an object possesses.– Fixed– Independent of the object’s

location

•Weight: A measure of the earth’s gravitational attraction for an object.– Not fixed– Depends on the object’s location.

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Measurement and

Significant Figures

Measurement and

Significant Figures

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Measurements

• Experiments are performed.

• Numerical values or data are obtained from these measurements.

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Form of a Measurement

70 kilograms = 154 pounds

numerical value

unit

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Significant Figures

• The number of digits that are known plus one estimated digit are considered significant in a measured quantity

estimated5.16143

known

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estimated6.06320

Significant Figures

• The number of digits that are known plus one estimated digit are considered significant in a measured quantity

known

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Significant Figures on Reading a Thermometer

Significant Figures on Reading a Thermometer

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Temperature is estimated to be 21.2oC. The last 2 is uncertain.

The temperature 21.2oC is expressed to 3 significant figures.

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Temperature is estimated to be 22.0oC. The last 0 is uncertain.

The temperature 22.0oC is expressed to 3 significant figures.

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461

All nonzero numbers are significant.

Significant Figures

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461

All nonzero numbers are significant.

Significant Figures

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461

All nonzero numbers are significant.

Significant Figures

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461

3 Significant Figures

All nonzero numbers are significant.

Significant Figures

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401

3 Significant Figures

A zero is significant when it is between nonzero digits.

Significant Figures

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A zero is significant when it is between nonzero digits.

5 Significant Figures

600.39

Significant Figures

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3 Significant Figures

30.9

A zero is significant when it is between nonzero digits.

Significant Figures

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A zero is significant at the end of a number that includes a decimal point.

5 Significant Figures

000.55

Significant Figures

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A zero is significant at the end of a number that includes a decimal point.

5 Significant Figures

0391.2

Significant Figures

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A zero is not significant when it is before the first nonzero digit.

1 Significant Figure

600.0

Significant Figures

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A zero is not significant when it is before the first nonzero digit.

3 Significant Figures

907.0

Significant Figures

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A zero is not significant when it is at the end of a number without a decimal point.

1 Significant Figure

00005

Significant Figures

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A zero is not significant when it is at the end of a number without a decimal point.

4 Significant Figures

01786

Significant Figures

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Scientific Notation of Numbers

Scientific Notation of Numbers

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• Very large and very small numbers are often encountered in science.

6022000000000000000000000.00000000000000000000625

• Very large and very small numbers like these are awkward and difficult to work with.

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602200000000000000000000

A method for representing these numbers in a simpler form is scientific notation.

0.00000000000000000000625

6.022 x 1023

6.25 x 10-21

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Scientific Notation

• Write a number as a power of 10

• Move the decimal point in the original number so that it is located after the first nonzero digit.

• Follow the new number by a multiplication sign and 10 with an exponent (power).

• The exponent is equal to the number of places that the decimal point was shifted.

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Write 6419 in scientific notation.

64196419.641.9x10164.19x1026.419 x 103

decimal after first nonzero

digitpower of 10

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Write 0.000654 in scientific notation.

0.0006540.00654 x 10-10.0654 x 10-20.654 x 10-3 6.54 x 10-4

decimal after first nonzero

digitpower of 10

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Significant Figures in Calculations

Significant Figures in Calculations

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The Metric System

The Metric System

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• The metric or International System (SI, Systeme International) is a decimal system of units.

• It is built around standard units.

• It uses prefixes representing powers of 10 to express quantities that are larger or smaller than the standard units.

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International System’s Standard Units of Measurement

Quantity Name of Unit Abbreviation

Length meter m

Mass kilogram kg Temperature Kelvin K

Time second sAmount of substance mole mol

Electric Current ampere A

Luminous Intensity candela cd

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Prefixes and Numerical Values for SI Units Power of 10

Prefix Symbol Numerical Value Equivalent

exa E 1,000,000,000,000,000,000 1018

peta P 1,000,000,000,000,000 1015

tera T 1,000,000,000,000 1012

giga G 1,000,000,000 109

mega M 1,000,000 106

kilo k 1,000 103

hecto h 100 102

deca da 10 101

— — 1 100

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Prefixes and Numerical Values for SI Units

deci d 0.1 10-1

centi c 0.01 10-2

milli m 0.001 10-3

micro 0.000001 10-6

nano n 0.000000001 10-9

pico p 0.000000000001 10-12

femto f 0.00000000000001 10-15

atto a 0.000000000000000001 10-18

Power of 10Prefix Symbol Numerical Value Equivalent

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Problem SolvingProblem Solving

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Dimensional Analysis

Dimensional analysis converts one unit to another by using conversion factors.

unit1 x conversion factor = unit2

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Basic Steps

1. Read the problem carefully. Determine what is to be solved for and write it down.

2. Tabulate the data given in the problem.– Label all factors and measurements with

the proper units.

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3. Determine which principles are involved and which unit relationships are needed to solve the problem.

– You may need to refer to tables for needed data.

4. Set up the problem in a neat, organized and logical fashion.

– Make sure unwanted units cancel. – Use sample problems in the text as

guides for setting up the problem.

Basic Steps

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5. Proceed with the necessary mathematical operations.

– Make certain that your answer contains the proper number of significant figures.

6. Check the answer to make sure it is reasonable.

Basic Steps

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Degree Symbols

degrees Celsius = oC

Kelvin (absolute) = K

degrees Fahrenheit = oF

Temperature Conversions

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o o oF - 32 = 1.8 x C

To convert between the scales use the following relationships.

o o oF = 1.8 x C + 32

oK = C + 273.15

oo F - 32C =

1.8

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It is not uncommon for temperatures in the Canadian planes to reach –60oF and below during the winter. What is this temperature in oC and K?

oo F - 32C =

1.8

o o60. - 32C = = -51 C

1.8

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It is not uncommon for temperatures in the Canadian planes to reach –60oF and below during the winter. What is this temperature in oC and K?

oK = C + 273.15

oK = -51 C + 273.15 = 222 K

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DensityDensity

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Density is the ratio of the mass of a substance to the volume occupied by that substance.

massd =

volume

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Mass is usually expressed in grams and volume in ml or cm3.

gd =

mL3

gd =

cm

The density of gases is expressed in grams per liter.

gd =

L

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Density varies with temperature

o

2

4 CH O

1.0000 g gd = = 1.0000

1.0000 mL mL

o

2

80 CH O

1.0000 g gd = = 0.97182

1.0290 mL mL

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ExamplesExamples

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A 13.5 mL sample of an unknown liquid has a mass of 12.4 g. What is the density of the liquid?

MD

V 0.919 g/mL12.4g

13.5mL

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46.0 mL

98.1 g

A graduated cylinder is filled to the 35.0 mL mark with water. A copper nugget weighing 98.1 grams is immersed into the cylinder and the water level rises to the 46.0 mL. What is the volume of the copper nugget? What is the density of copper?

35.0 mL

copper nugget final initialV = V -V = 46.0mL - 35.0mL = 11.0mL

g/mL8.92mL11.0g98.1

VM

D

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The density of ether is 0.714 g/mL. What is the mass of 25.0 milliliters of ether?

Method 1 (a) Solve the density equation for mass.

massd =

volume

(b) Substitute the data and calculate.

mass = density x volume

0.714 g25.0 mL x = 17.9 g

mL

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The density of ether is 0.714 g/mL. What is the mass of 25.0 milliliters of ether?

Method 2 Dimensional Analysis. Use density as a conversion factor. Convert:

0.714 g25.0 ml x = 17.9 g

mL

mL → g

gmL x = g

mLThe conversion of units is

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The density of oxygen at 0oC is 1.429 g/L. What is the volume of 32.00 grams of oxygen at this temperature?

Method 1

(a) Solve the density equation for volume.

massd =

volume

(b) Substitute the data and calculate.

massvolume =

density

2

2

32.00 g Ovolume = = 22.40 L

1.429 g O /L

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The density of oxygen at 0oC is 1.429 g/L. What is the volume of 32.00 grams of oxygen at this temperature?

Method 2 Dimensional Analysis. Use density as a conversion factor. Convert:

2 22

1 L32.00 g O x = 22.40 L O

1.429 g O

g → L

Lg x = L

gThe conversion of units is

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