C H A P T E R 3

SCIENTIFIC MEASUREMENT

WHAT IS MEASUREMENT?

• Comparing one object to a standard

• In science, we use SI Units

• meters, oC, grams NOT oF, pounds, ounces etc.

TWO TYPES OF MEASUREMENTS

1. Qualitative = descriptive and non-numerical

• EX: color, odor, texture, etc

2. Quantitative = definite form, numbers and units

• EX: temperature, mass, length, volume, density

SCIENTIFIC NOTATION

• Used to write very big and very small numbers

• 6.02 X 1023 instead of 602000000000000000000000

• Number is written as the product of 2 numbers: a

coefficient and 10 raised to a power

• N X 10x

• N is a coefficient; a number that is between 1 and ten

• X is an integer

SCIENTIFIC NOTATION RULES

• Only one digit to the left of the decimal

• Exponents

• if the # is greater than one, the exponent is positive

• if the # is less than one, the exponent is negative

• In your calculator, use “EE” or “EXP” for the “x 10 ^”

• EX: 6.02 x 1023 in calculator = 6.02 EE 23

2 500 000 000

Step #1: Insert an understood decimal point

.

Step #2: Decide where the decimal must end

up so that one number is to its left

Step #3: Count how many places you bounce

the decimal point

1 2 3 4 5 6 7 8 9

Step #4: Re-write in the form M x 10n

2.5 X 109

CONVERTING A NUMBER INTO SCIENTIFIC NOTATION

The exponent is

the number of

places we

moved the

decimal.

CONVERTING A NUMBER INTO SCIENTIFIC NOTATION

The exponent is positive because the

number we started with was greater

than 1.

2 500 000 000

2.5 X 109

CONVERTING A NUMBER INTO SCIENTIFIC NOTATION

Step #1 Locate the decimal

Step #2 Decide where the decimal must end up so that

one number is to its left

Step #3 count how many places you bounce the

decimal point

Step #4 Re-write in the form N x 10x

1 2 3 4 5

CONVERTING A NUMBER INTO SCIENTIFIC NOTATION

The exponent is negative because the

number we started with was less than 1.

CHEM-LOG…CONVERT THE FOLLOWING

• 45000 written as

• 510 written as

• 602000 written as

• 4.5 x 10 -4 written as

• 3.2 x 10 -2 written as

• 2.89 x 10 -3 written as

4.5 x 10 4

5.3 x 10 2

6.02 x 10 5

0.00045

0.032

0.00289

If you moved the decimal point to the left, your exponent is positive

If you moved to the right, your exponent is negative

YOUR TURN

PRACT ICE US ING SCIENT IF IC NOTAT ION…PAGE

PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION

• Addition and Subtraction

• If the exponents are the same, add the coefficients

• Keep the exponent the same in the answer

PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION

• Addition and Subtraction

• If the exponents are NOT the same, we must first move

a decimal to make them the same

• Keep the exponent the same in the answer

PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION

• GET USED TO USING YOUR CALCULATOR…

2.5 x 104 x 3.2 x 108

5.7 x 104 ÷ 8.9 x 108

PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION

• GET USED TO USING YOUR CALCULATOR…

2.5 x 10-7 x 3.2 x 10-2

5.7 x 10-3 ÷ 8.9 x 10-1

UNCERTAINTY IN MEASUREMENT

• Accuracy = a measure of how close a

measurement comes to the actual or true value of

whatever is measured

• Precision = a measure of how close a series of

measurements are to one another

Precise, not

accurate

UNCERTAINTY IN MEASUREMENT

Accurate, not

precise

UNCERTAINTY IN MEASUREMENT

Not precise,

not accurate

UNCERTAINTY IN MEASUREMENT

Precise AND

accurate

ERROR IN MEASUREMENT

• Accepted/actual value = the correct value based

on reliable references

• Experimental value = the value measure in the lab

• Error = accepted – experimental

• % error = I accepted – experimental I x 100

accepted

CALCULATING ERROR

• If you only make 33 cookies and the recipe says you

should make 36, what is your percent error?

Percent Error = I accepted – experimental I x 100

accepted

accepted = 36

experimental = 33

Percent Error = I 36-33 I x 100

36

= 8.3 % error

SIGNIFICANT FIGURES

• Numbers that include ALL digits that can be known

plus a last digit that is estimated

• Digits that have meaning

SIGNIFICANT FIGURES

•Rules regarding zeros • Every non-zero digit is significant (567)

• Zeros between non-zeros are sig (305)

• Zeros in front of nonzeros are

placeholders…NOT SIG (0.00035)

• Zeros following a nonzero only sig if • The come after a decimal point (3.4210)

• Or a decimal follows (3420.)

• 3420

SIGNIFICANT FIGURES

• HOW MANY SIG FIGS??????

4.21

4.210

0.0421

42.10

4210

42010

42010.0

(3)

(4)

(4)

(3)

(3)

(4)

(6)

SIGNIFICANT FIGURES IN CALCULATIONS

• How many significant figures do you need to give in

your answer?

• Answers cannot be more precise than the least

precise measurement

• FOR EXAMPLE, divide 21.4 by 9.8…what’s your answer?

• Answer in calculator says 2.183673469

SIGNIFICANT FIGURES IN CALCULATIONS

• Adding and subtracting • The last digit in your answer is set by the first doubtful digit

• For Example:

0.200

1.2

+ 3.400

4.800

Answer should

only have one

significant digit

to the right of the decimal

point

Therefore, the

answer should

be

4.8

SIGNIFICANT FIGURES IN CALCULATIONS

• Multiplying and dividing

• Answer contains no more sig figs that the least accurate

measurement

• For example:

3.2 x 7.81542 = 25.009344

Answer should

only have two

sig figs

Therefore, the

answer should

be

25

SIGNIFICANT FIGURES IN CALCULATIONS

Rounding

• If the digit immediately following the last sig fig is less

than 5, drop all digits after the last sig fig

• If the digit is 5 or greater, the value of the digit in the

last sig place is increased (rounded) by 1

0.1710

1.2

+ 3.490

4.8610

Answer should

only have one

significant digit

to the left of the decimal point

The number that

follows the 8 is

greater than 5 so

drop it…answer is 4.9

YOUR TURN

PRACT ICE S IG F IGS IN PACKET… PAGES 12/13

FINISH FOR HOMEWORK!!!

INTERNATIONAL SYSTEM OF UNITS (SI)

• Revised version of the metric system

• Seven base units

• length, mass, temp, time, amount, light intensity, electric current

• Derived units can be calculated using base units

• density, volume, pressure

SI UNITS

• Length: meter (m)

• Mass: kilogram (kg)

• Temperature: kelvin (K)

• Time: second (s)

• Quantity: mole (mol)

• Luminosity: candela (cd)

• Current: ampere (A)

DERIVED UNITS - VOLUME

• Volume = the space occupied by any sample of

matter

• Derived from length measurements

• V = l x w x h

• Can also be measured by volume displacement

• Units

• cubic meter (m3) or cubic cm (cm3)

• 1cm3 = 1ml

DERIVED UNITS - DENSITY

• Defined: ratio of an object’s mass to its volume

• Equation: D = m/V

• Units: g/cm3

DENSITY PROBLEM #1

• A copper penny has a mass of 3.1 g and a volume

of 0.35 cm3. What is the density of copper?

Equation: D = m/V

Units: g/cm3

DENSITY PROBLEM #2

• A student finds a shiny piece of metal that she thinks is

aluminum. In the lab, she determines that the metal has

a volume of 245 cm3 and a mass of 612 g. Calculate the

density. Is it aluminum? Density Al= 2.70 g/cm3

Equation: D = m/V

Units: g/cm3

TEMPERATURE

• Defined: direction of heat transfer

• When two objects are in contact, heat moves from the object

at the higher temperature to the object at the lower

temperature

TEMPERATURE SCALES

• Celsius

• Uses two determined temperatures as reference temp

• Boiling point of water = 100oC

• Freezing point of water = 0 oC

• Kelvin scale

• Boiling point of water = 373 K

• Freezing point of water = 273 K

• Notice no degree sign

• 0 K = absolute zero or the point at which all motion stops

CONVERTING BETWEEN CELSIUS AND KELVIN

K = oC + 273

Ex: convert 25 oC to K

K = 25 oC + 273

K = 298K

oC = K - 273

Ex: convert 0K to oC

oC = 0K - 273

oC = -273 oC

HOMEWORK FOR TONIGHT

CH3 EOC Questions

# 36, 39, 40-42, 44, 49, 52, 61, 70, 81

C H A P T E R 4

DIMENSIONAL ANALYSIS

METRIC SYSTEM

• Americans measure in feet, inches, yards, etc.

• Based on the king

• Yard = length of the king’s arm

• Foot = length of the king’s foot

• Pound = amount of marble the king could pick up with one hand

• New king = new standards

• The rest of the world measure using the metric system

• Based on powers of 10

METRIC PREFIXES

Prefix Symbol Scientific

Notation

Meaning

Mega- M 106 Million times

kilo- k 103 thousand times

hecto- h 102 Hundred times

deca- da 101 Ten times

BASE ~ ~ Base Unit

deci- d 10-1 1 / tenth

centi- c 10-2 1 / hundredth

milli- m 10-3 1 / thousandth

METRIC PREFIXES

Prefix Symbol Scientific

Notation

Pnemonic Device

Mega- M 106 Most

kilo- k 103 Kittens

hecto- h 102 Hate

deca- da 101 Dogs

BASE ~ ~ Because

deci- d 10-1 Dogs

centi- c 10-2 Can’t

milli- m 10-3 Meow !

DIMENSIONAL ANALYSIS

• a way to analyze and solve problems using the units

or dimensions of the measurements

CONVERSION FACTOR

• Relationships between two measurements that

allow you to convert from one unit to another

• Ex: 1 yr = 365 days, 1 day = 24 hours

3 STEPS TO SOLVING PROBLEMS

ACE Method

1. Analyze

• Identify what is given, unknown, make a plan

2. Calculate

• Substitute values and use algebra to solve

3. Evaluate

• Does the answer make sense?

SAMPLE PROBLEM #1

How many days are there in 6 weeks?

You are looking

for this!

This is your “given”.

ANALYZE

Figure out what relationships you

will have to know in order to

convert from 1 unit to another.

1 week = 7 days

SET UP

Start with given and work toward what you are looking for.

6weeks = ? days

CONVERSION FACTOR

Conversion Factor : top and bottom must be

equal in value

days week 1

days 7x weeks 6

CANCELING UNITS

6 weeks x = 42 days 1 week

7 days

Cancel units : cancel

units to leave correct

units for the answer

Calculate : multiply

across top and bottom

and divide to get final

answer

SAMPLE PROBLEM #2

• If you are traveling 65 miles per hour,

how far will you go in 4 hours?

SET UP THE PROBLEM

• Given: 4 hours, 65 miles = 1 hour

• Unknown: how many miles?

• ANALYZE the DIMENSIONS

If you have hours and want miles, your conversion

factor should be arranged to CANCEL hours and

LEAVE miles

SAMPLE PROBLEM #2

1. Write your Given “over one” 4 hours

1

2. “times a line” 4 hours x _______

1

3. To cancel hours, the conversion factor must have hours on the BOTTOM

4 hours x _______

1 1 hour

4. Conversion factor must have desired unit on TOP

4 hours x 65 miles 1 1 hour

= 260 miles

SAMPLE PROBLEM #3

• If you just turned 17 years old, how many seconds

old are you?

Given: 17 years old

Unknown: seconds old

Conversion factors: 1 yr = 365.25 days 1 day = 24 hrs 1 hr = 60 min 1 min = 60 s

SAMPLE PROBLEM #3

• Solve:

17 yr x 365.25 day x 24 hr x 60 min x 60 s =

1 yr 1 day 1 hr 1 min

When solving dimensional analysis problems, multiply by everything in the numerator and then divide by everything in the denominator and hit enter only ONCE!!

In calculator:

17 x 365.25 x 24 x 60 x 60 ÷ 1 ÷ 1 ÷ 1 ÷ 1 =

SAMPLE PROBLEM #3

•Answer: 17 yrs = 536,479,200 s

•Check: Does this answer make

sense?

• Yes! 17 years should be a lot of

seconds!

SAMPLE PROBLEM #4

• If you are traveling 50 miles per hour, how many

feet per second are you going?

Given: 50 miles per hour

Unknown: feet per second

Conversion factors: 1 mile = 5280 ft 1 hr = 60 min 1 min = 60 s

SAMPLE PROBLEM #4

• Solve:

50 miles x 5280 feet x 1 hrx x 1 min=

1 hour 1 mile 60 min 60 sec

In calculator:

50 x 5280 x 1 x 1 ÷ 1 ÷ 1 ÷ 60 ÷ 60 = 73 feet/sec

SAMPLE PROBLEM #5

• The average American student is in class 330

minutes/day. How many hours a year is this if you

have perfect attendance (181 days)?

Given: 330 minutes/day; 181 days

Unknown: hours a year

Conversion factors: 1 day = 24 hours 1 hr = 60 min