Measurements Chapter 1. Units of Measurement You are making a measurement when you Check you weight Read your watch Take your temperature Weigh a cantaloupe.

MeasurementsChapter 1

Units of Measurement

You are making a measurement when you

Check you weight

Read your watch

Take your temperature

Weigh a cantaloupe

What kinds of measurements did you make today?

Standards of Measurement

When we measure, we use a measuring tool to compare some dimension of an object to a standard.

Some Tools for Measurement

Learning Check

From the previous slide, state the tool (s) you would use to measure

A. temperature ____________________

B. volume ____________________

____________________

C. time ____________________

D. weight ____________________

Solution

From the previous slide, state the tool (s) you would use to measure

A. temperature thermometer

B. volume measuring cup, graduated cylinder

C. time watch

D. weight scale

Measurement in Chemistry

In chemistry we

do experiments

measure quantities

use numbers to report measurements

Stating a Measurement

In every measurement there is a

Number

followed by a

Unit from measuring device

Learning Check

What is the unit of measurement in each of the following

examples?

A. The patient’s temperature is 102°F.

B. The sack holds 5 lbs of potatoes.

C. It is 8 miles from your house to school.

D. The bottle holds 2 L of orange soda.

Metric System (SI)

Is a decimal system based on 10 Used in most of the world Used by scientists and hospitals

Units in the Metric System

length meter m

volume liter L

mass gram

g

temperature Celsius

°C

Learning Check

Identify the measurement in metric units.

A. John’s height is

1) 1.5 yards 2) 6 feet 3) 2 meters

B. The volume of saline in the IV bottle is

1) 1 liters 2) 1 quart 3) 2 pints

C. The mass of a lemon is

1) 12 ounces 2) 145 grams 3) 0.6 pounds

Measurements

Measured Numbers and Significant Figures

Measured Numbers

When you use a measuring tool to determine a quantity such as your height or weight, the numbers you obtain are called measured numbers.

Reading a Meterstick

. l2. . . . I . . . . I3 . . . .I . . . . I4. . cm

First digit (known)= 2 2.?? cm

Second digit (known) = 0.7 2.7? cm

Third digit (estimated) between 0.05- 0.07

Length reported = 2.75 cm

or 2.76 cm

or 2.77 cm

Known + Estimated Digits

Known digits 2 and 7 are 100% certain

The third digit 6 is estimated (uncertain)

In the reported length, all three digits

(2.76 cm) are significant including the estimated

one

Learning Check

. l8. . . . I . . . . I9. . . .I . . . . I10. . cm

What is the length of the line?

1) 9.2 cm

2) 9.22 cm

3) 9.23 cm

How your answer compare with your neighbor’s

answer? Why or why not?

Learning Check

l5. . . . I . . . . I6. . . .I . . . . I7. . cm

What is the length of the line?

1) 6.0 cm

2) 6.06 cm

3) 6.60 cm

Zero as a Measured Number

. l3. . . . I . . . . I4 . . . . I . . . . I5. . cm

What is the length of the line?

First digit 4.?? cm

Second digit 4.5? cm

Last (estimated) digit is 4.50 cm

(not to the left or right of .5)

Exact Numbers Obtained when you count objects

2 soccer balls

1 watch

4 pizzas Obtained from a defined relationship

1 foot = 12 inches

1 meters = 100 cm Not obtained with measuring tools

Learning Check A. Exact numbers are obtained by

1. measuring

2. counting3. definition

B. Measured numbers are obtained by

1. measuring

2. counting

3. definition

Learning Check

Classify each of the following as an exact (1)

or a measured (2) number.

A.___Gold melts at 1064°C

B.___1 yard = 3 feet

C.___A red blood cell with diameter 6 x 10-4 cm

D.___There were 6 hats on the shelf

E.___A can of soda contains 355 mL of soda

Significant Figures in Measurement

The numbers reported in a measurement are limited by the measuring tool

Significant figures in a measurement include the known digits plus one estimated digit

1.8

•Any digit that is not zero is significant

1.234 kg 4 significant figures

•Zeros between nonzero digits are significant

606 m 3 significant figures

•Zeros to the left of the first nonzero digit are not significant

0.08 L 1 significant figure

•If a number is greater than 1, then all zeros to the right of the decimal point are significant

2.0 mg 2 significant figures

•If a number is less than 1, then only the zeros that are at the end and in the middle of the number are significant

0.00420 g 3 significant figures

Significant Figures Summary

Counting Significant Figures

Number of Significant Figures

38.15 cm 4

5.6 ft 2

65.6 lb ___

122.55 m ___

Complete: All non-zero digits in a measured number are (significant or not significant).

Leading Zeros

Number of Significant Figures

0.008 mm 1

0.0156 oz 3

0.0042 lb ____

0.000262 mL ____

Complete: Leading zeros in decimal numbers are

(significant or not significant).

Sandwiched Zeros

Number of Significant Figures

50.8 mm 3

2001 min 4

0.702 lb ____

0.00405 m ____

Complete: Zeros between nonzero numbers are

(significant or not significant).

Trailing Zeros

Number of Significant Figures

25,000 in. 2

200 yr 1

48,600 gal 3

25,005,000 g ____

Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders.

Learning Check

A. Which answers contain 3 significant figures?

1) 0.4760 2) 0.00476 3) 4760

B. All the zeros are significant in

1) 0.00307 2) 25.300 3) 2.050 x 103

C. 534,675 rounded to 3 significant figures is

1) 535 2) 535,000 3) 5.35 x

105

Learning Check

In which set(s) do both measured numbers contain the same number of significant figures?

1) 22.0 and 22.00

2) 400.0 and 40

3) 0.000015 and 150,000

State the number of significant figures in each of the following measured/calculated numbers:

A. 0.030 m 1 2 3

B. 4.050 L 2 3 4

C. 0.0008 g 1 2 4

D. 3.00 m 1 2 3

E. 2,080,000 bees 3 5 7

Learning Check SF3

Significant Numbers in Calculations

A calculated answer cannot be more precise than the measuring tool.

A calculated answer must match the least precise measurement.

Significant figures are needed for final answers from

1) adding or subtracting

2) multiplying or dividing

Adding and Subtracting

The answer has the same number of decimal places as the measurement with the fewest decimal places.

25.2 one decimal place

+ 1.34 two decimal places

26.54

answer 26.5 one decimal place

E.g., 25 + 6.022 = 31

Learning Check

In each calculation, round the answer to the correct number of significant figures.

A. 235.05 + 19.6 + 2.1 =

1) 256.75 2) 256.8 3) 257

B. 58.925 - 18.2 =

1) 40.725 2) 40.73 3) 40.7

Multiplying and Dividing

Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

Learning Check

A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198

B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60

C. 2.54 X 0.0028 =

0.0105 X 0.060

1) 11.3 2) 11 3) 11.041

Measurements

Prefixes and

Equalities

Metric Prefixes

Increase or decrease basic unit by 10

Form new units larger or smaller than the basic

units

Indicate a numerical value

prefix = value

1 kilometer = 1000 meters

1 kilogram = 1000 grams

Prefixes that Increase A Unit

Prefix Symbol Value

giga- G 1 000 000 000

mega- M 1 000 000

kilo- k 1 000

Prefixes that Decrease A Unit

Prefix Symbol Value

deci- d 0.1centi- c 0.01milli- m 0.001micro- (mu) 0.000 001nano n 0.000 000 0001

Learning Check

Match 1) length 2) mass 3) volume

____ A. A bag of tomatoes is 4.6 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

Select the unit you would use to measure A. Your height

1) millimeters 2) meters 3) kilometers

B. Your mass

1) milligrams 2) grams 3) kilograms

C. The distance between two cities

1) millimeters 2) meters 3) kilometers

D. The width of an artery

1) millimeters 2) meters 3) kilometers

Learning Check

Indicate the prefix to use for

1. A mass that is 1000 times greater than 1 gram

1) kilo 2) milli 3) mega

2. A length that is 1/100 of 1 meter?

1) deci 2) centi 3) milli

3. A unit of time that is 1/1000 of a second.

1) nanosecond 2) microsecond 3)millisecond

Equalities State the same measurement in two different units

length

10.0 in.

25.4 cm

Fundamental & Derived SI units and Metric EqualitiesLength 1 km = 1000 m 1m = 100 cm1m = 100 cm 1m = 1000 mm

Mass 1 kg = 1000 g1 kg = 1000 g 1 g =

Volume 1 kL = 1000 L 1L = 100 cL 1L = 1000 mL

Matter is anything that takes up space and has mass

Fundamental SI Units (Derived SI units are derived from these base units):

Volume – SI derived unit for volume is cubic meter (m3)

1 cm3 = (1 x 10-2 m)3 = 1 x 10-6 m3

1 dm3 = (1 x 10-1 m)3 = 1 x 10-3 m3

1 L = 1000 mL = 1000 cm3 = 1 dm3

1 mL = 1 cm3

A. 1000 m = 1 ___ 1) mm 2) km 3) dm

B. 0.001 g = 1 ___ 1) mg 2) kg 3) dg

C. 0.1 L = 1 ___ 1) mL 2) cL 3) dL

D. 0.01 m = 1 ___ 1) mm 2) cm 3) dm

Learning Check

Give the value of the following units:

A. 1 kg = ____ g

1) 10 g 2) 100 g 3) 1000 g

B. 1 mm = ____ m

1) 0.001 m 2) 0.01 m 3) 0.1 m

Learning Check

Some American Equalities

1 ft = inches

1 lb = 16 oz

1 quart = pints

1 quart = 4 cups

Why are the quantities in each pair equal?

Some Metric-American Equalities

1 in. = 2.54 cm

1 qt = 946 mL

1 L = 1.06 qt

1 lb = 454 g

1 kg = 2.20 lb

Remember these for exams.

Equalities given in a Problem

Example 1

At the store, the price of one pound of red peppers is

$2.39.

Equality: 1 lb red peppers = $2.39

Example 2

At the gas station, one gallon of gas is $1.34.

Equality: 1 gallon of gas = $1.34

Accuracy – how close a measurement is to the true value

Precision – how close a set of measurements are to each other

accurate&

precise

precisebut

not accurate

not accurate&

not precise

Accuracy vs. Precision

Conversion Factors

Fractions in which the numerator and denominator are quantities expressed in an equality between those units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm

2.54 cm 1 in.

Learning Check

Write conversion factors that relate each of the following pairs of units:

A. Liters and mL

B. Hours and minutes

D. Meters and kilometers

Solution

A. quarts and mL 1 L = 1000 mL

1 L and 1000 mL

1000 mL 1 L

B. hours and minutes 1 hr = 60 min

1 hr and 60 min

60 min 1 hr

C. meters and kilometers 1 km = 1000 m

1 km and 1000 m

1000 m 1 km

Measurements

Problem Solving Using Conversion Factors

Initial and Final Units

1. A person has a height of 2.0 meters. What is

that height in inches?

Initial unit = m Final unit = _______

2) Blood has a density of 1.05 g/mL. If a person

lost 0.30 pints of blood at 18°C, how many ounces

of blood would that be?

Initial = pints Final unit = _______

inches

ounces

How many minutes are in 2.5 hours?

Initial unit

2.5 hr

Conversion Final

factor unit

2.5 hr x 60 min = 150 min

1 hr

cancel Answer (2 SF)

Learning Check

A rattlesnake is 2.44 m long. How long is the snake in cm?

1) 2440 cm

2) 244 cm

3) 24.4 cm

Solution

A rattlesnake is 2.44 m long. How long is the snake in cm?

2) 244 cm

2.44 m x 100 cm = 244 cm

1 m

Learning Check

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x 24 hr x ??

1 day

Solution CF2

Unit plan: days hr min seconds

2 SF Exact

1.4 day x 24 hr x 60 min x 60 sec

1 day 1 hr 1 min

= 1.2 x 105 sec

Unit Check

What is wrong with the following setup?

1.4 day x 1 day x 60 min x 60 sec

24 hr 1 hr 1 min

Unit Check

1.4 day x 1 day x 60 min x 60 sec

24 hr 1 hr 1 min

Units = day2-sec/hr2 Not the final unit needed

Learning Check An adult human has 4650 mL of blood. How many gallons of blood is that?

Unit plan: mL qt gallon

Equalities: 1 quart = 946 mL

1 gallon = 4 quarts

Your Setup:

Solution

Unit plan: mL qt gallon

Setup:

4650 mL x 1 qt x 1 gal = 1.23 gal

946 mL 4 qt

3 SF equality exact 3 SF

Steps to Problem Solving

Read problem Identify data Write down a unit plan from the initial unit

to the desired unit Select conversion factors Change initial unit to desired unit Cancel units and check Do math on calculator Give an answer using correct significant figures

Learning Check

If the ski pole is 3.0 feet in length, how long is the ski pole in mm?

Solution

3.0 ft x 12 in x 2.54 cm x 10 mm =

1 ft 1 in. 1 cm

Learning Check

If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet?

Initial

8450 ft x 12 in. x 2.54 cm x 1 m

1 ft 1 in. 100 cm

x 1 min x 60 sec = 2400 sec

65 m 1 minfinal (2 SF)

Solution

Measurements

Density

Density

Density compares the mass of an object to its volume

D = mass = g or g

volume mL cm3

Note: 1 mL = 1 cm3

Learning Check D1

Osmium is a very dense metal. What is its

density in g/cm3 if 50.00 g of the metal occupies

a volume of 2.22cm3?

1) 2.25 g/cm3

2) 22.5 g/cm3

3) 111 g/cm3

Solution

2) Placing the mass and volume of the osmium metal into the density setup, we obtain

D = mass = 50.00 g = volume 2.22 cm3

= 22.522522 g/cm3 = 22.5 g/cm3

Volume Displacement

A solid displaces a matching volume of water when the solid is placed in water.

33 mL

25 mL

Learning Check

What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL?

1) 0.2 g/ cm3 2) 6 g/m3 3) 252 g/cm3

33 mL

25 mL

Solution 2) 6 g/cm3

Volume (mL) of water displaced = 33 mL - 25 mL = 8 mL

Volume of metal (cm3) = 8 mL x 1 cm3 = 8 cm3

1 mLDensity of metal =

mass = 48 g = 6 g/cm3

volume 8 cm3

Learning Check3

Which diagram represents the liquid layers in the cylinder?

(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)

1) 2) 3)

K

K

W

W

W

V

V

V

K

Density as Conversion Factors

A substance has a density of 3.8 g/mL.

Density = 3.8 g/mL

Equality 3.8 g = 1 mL

Conversion factors.

3.8 g and 1 mL

1 mL 3.8 g

Density Connections

Mass Volume

kg L

g mL (cm3)

mg

Learning Check

The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?

1) 0.614 kg

2) 614 kg

3) 1.25 kg

Solution

1) 0.614 kg

Unit plan: mL g kg

Equalities: 1 mL = 0.702 g and 1 kg = 1000 g Setup:

875 mL x 0.702 g x 1 kg = 0.614 kg

1 mL 1000 gdensity metric

factor factor

Learning Check

If blood has a density of 1.05 g/mL, how many liters of blood are donated if 575 g of blood are given?

1) 0.548 L

2) 1.25 L

3) 1.83 L

Solution

1)

Unit Plan: g mL L

575 g x 1 mL x 1 L = 0.548 L

1.05 g 1000 mL

Learning Check

A group of students collected 125 empty aluminum cans to take to the recycling center. If 21 cans make 1.0 pound of aluminum, how many liters of aluminum (D=2.70 g/cm3) are obtained from the cans?

1) 1.0 L 2) 2.0 L 3) 4.0 L

Solution

1) 1.0 L

125 cans x 1.0 lb x 454 g x 1 cm3

21 cans 1 lb 2.70 g

x 1 mL x 1 L = 1.0 L

1 cm3 1000 mL

Learning Check

You have 3 metal samples. Which one will displace the greatest volume of water?

1 2 3

Discuss your choice with another student.

25 g Al2.70 g/mL

45 g of gold19.3 g/mL

75 g of Lead11.3 g/mL

Solution

1) 25 g Al x 1 mL = 9.2 mL 2.70 g

25 g Al2.70 g/mL

Chapter 1

Measuring Temperature

Temperature

Particles are always moving. When you heat water, the water molecules move faster.

When molecules move faster, the substance gets hotter.

When a substance gets hotter, its temperature goes up.

Learning Check

Suppose you place water in a freezer.A. The water particles move

1) faster 2) slower 3) the same

B. The water will get

1) hotter 2) colder 3) stay the same

C. The temperature of the water will be

1) higher 2) lower 3) the same

Temperature

Measures the hotness or coldness of an object

Determined by using a thermometer that contains a

liquid that expands with heat and contracts with

cooling.

Temperature Scales

Units of Temperature between Boiling and Freezing

Fahrenheit Celsius Kelvin

Water boils 212°F 100°C 373 K

180° 100°C 100K

Water freezes 32°F 0°C 273 K

Learning Check

A. Temperature of freezing water

1) 0°F 2) 0°C 3) 0 K

B. Temperature of boiling water

1) 100°F 2) 32°F 3) 373K

C. Number of Celsius units between the

boiling and freezing points of water

1) 100 2) 180 3) 273

Fahrenheit Formula

180°F = 9°F = 1.8°F 100°C 5°C 1°C

Zero point: 0°C = 32°F

°F = 9/5 (T°C) + 32

or

°F = 1.8 (T°C) + 32

Celsius Formula

Rearrange to find T°C

°F = 1.8 T°C + 32

°F - 32 = 1.8 T°C ( +32 - 32)

°F - 32 = 1.8 T°C

1.8 1.8

°F - 32 = T°C

1.8

Temperature Conversions

A person with hypothermia has a body temperature of 29.1°C. What is the body temperature in °F?

°F = 1.8 (29.1°C) + 32 exact tenth's exact

= 52.4 + 32

= 84.4°F tenth’s

Learning Check

The normal temperature of a chickadee is 105.8°F. What is that temperature in °C?

1) 73.8 °C

2) 58.8 °C

3) 41.0 °C

Solution

3) 41.0 °C

Solution:

°C = (°F - 32)

1.8

= (105.8 - 32)

1.8

= 73.8°F

1.8° = 41.0°C

Learning Check

Pizza is baked at 455°F. What is that in °C?

1) 437 °C

2) 235°C

3) 221°C

Learning Check

On a cold winter day, the temperature falls to -15°C. What is that temperature in °F?

1) 19 °F

2) 59°F

3) 5°F

Kelvin Scale

On the Kelvin Scale

1K = 1°C

0 K is the lowest temperature

0 K = - 273°C

K °C

K = °C + 273

Learning Check

What is normal body temperature of 37°C in kelvins?

1) 236 K

2) 310 K

3) 342 K

Three States of Matter

solidliquid

gas

Physical or Chemical?

A physical change does not alter the composition or identity of a substance.

A chemical change alters the composition or identity of the substance(s) involved.

ice meltingsugar dissolving

in water

hydrogen burns in air to form water

Phase Change

An extensive property of a material depends upon how much matter is is being considered.

An intensive property of a material does not depend upon how much matter is being considered.

• mass

• length

• volume

• density

• temperature

• color

Extensive and Intensive Properties

Matter - anything that occupies space and has mass.

mass – measure of the quantity of matter

SI unit of mass is the kilogram (kg)

1 kg = 1000 g = 1 x 103 g

weight – force that gravity exerts on an object

weight = c x mass

on earth, c = 1.0

on moon, c ~ 0.1

A 1 kg bar will weigh

1 kg on earth

0.1 kg on moon