chemistry 103 lecture 2. outline i. sig figs – identification – rounding – math operations ii....

Chemistry 103

Lecture 2

Outline

• I. Sig Figs – Identification– Rounding– Math Operations

• II. Mathematics of Chemistry– Scientific Notation– Dimensional Analysis

Periodic Table - Elements to Memorize

Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings

Significant FiguresAre the digits in any measurement known with certainty, plus one digit that is uncertain.

Measured numbers convey

*Magnitude*Units

*Precision

The Calculator Problem

7.83.8

The Calculator Problem

7.83.8

Calculator Answer: 2.05263……

Rules for Significant Figures

It’s ALL about the ZEROs

Rules for Sig Figs

• All non-zero numbers in a measurement are significant.

4573

4573 has 4 sig figs

Rules for Sig Figs

• All zeros between sig figs are significant.

23007

23007 has 5 sig figs

Rules for Sig Figs

• In a number less than 1, zeros used to fix the position of the decimal are not significant.

0.000210.00021 has 2 sig figs

Rules for Sig Figs

• When a number has a decimal point, zeros to the right of the last nonzero digit are significant

0.00021000.0002100 has 4 sig figs

Rules for Sig Figs

• When a number has a decimal point, zeros to the right of the last nonzero digit are significant

3400.3400. has 4 sig figs

Rules for Sig Figs

• When a number without a decimal point explicitly shown ends in one or more zeros, we consider these zeros not to be significant. If some of the zeros are significant, bar notation is used.

_

820000 meters 3 sig figs 820000

Practice Identifying Sig Figs

Significant FiguresHow many assuming all numbers are measured?

a). 75924

b). 30.002

c). 0.004320

d). 0.000002

e). 46,000

Significant FiguresHow many assuming all numbers are measured?

a). 75924 (5 sig figs)

b). 30.002 (5 sig figs)

c). 0.004320 (4 sig figs)

d). 0.000002 (1 sig fig)

e). 46,000 (2 sig figs)

Rounding off Numbers

• The number of significant figures in measurements affects any calculations done with these measurements– Your calculated answer can only be as certain

as the numbers used in the calculation

Calculator: Friend or Foe?

• Sometimes, the calculator will show more (or fewer) significant digits than it should– If the first digit to be deleted is 4 or

less, simply drop it and all the following digits

– If the first digit to be deleted is 5 or greater, that digit and all that follow are dropped and the last retained digit is increased by one

Sig Fig Rounding Example:

• Round the following measured number to

4 sig figs:

• 82.56702

Sig Fig Rounding Example


4 sig figs:

• 82.56702

Sig Fig Rounding Example


4 sig figs:

• 82.56702 ANSWER: 82.57

Adding Significant Zeros• Sometimes a calculated answer requires more significant

digits. Then one or more zeros are added.

Calculated Answer Zeros Added to Give 3 Significant Figures

4 4.001.5 1.500.2 0.200

12 12.0

Practice Rounding Numbers

Significant FiguresRound each to 3 sig figs

a). 28.394

b). 0.000230600

c). 2568

d). 2562

e). 8

Significant FiguresRound each to 3 sig figs

a). 28.394 ANSWER: 28.4

b). 0.000230600 ANSWER: 0.000231

c). 2568 ANSWER: 2570

d). 2562 ANSWER: 2560

e). 8 ANSWER: 8.00

Math Operations & Sig Figs

When multiplying or dividing, use

• The same number of significant figures in your final answer as the measurement with the fewest significant figures.

• Rounding rules to obtain the correct number of significant figures.

Example:

110.5 x 0.048 = 5.304 = 5.3 (rounded)

4 SF 2 SF calculator 2 SF

Multiplication and Division

When adding or subtracting, use

• The same number of decimal places in your final answer as the measurement with the fewest decimal places (least precise measurement).

• Use rounding rules to adjust the number of digits in the answer.

25.2 one decimal place

+ 1.34 two decimal places

26.54 calculated answer

26.5 answer with one decimal place

Addition and Subtraction

Report Answer with Correct Number of Sig Figs

A). 124.54 x 2.2 =

B). 3420. + 2400. + 1095 =

C). 98.5564 = 45.68

When Math Operations Are Mixed

If you have both addition/subtraction and multiplication/division in a formula,

-carry out the operations in parenthesis first, and round according to the rules for that type of operation.

-complete the calculation by rounding according to the rules for the final type of operation.


_____5.681g_____ =(52.15ml - 32.4ml)


_____5.681g_____ =(52.15ml - 32.4ml)

-carry out the operations in parenthesis first, and round according to the rules for that type of operation.


_____5.681g_____ = 5.681g(52.15ml - 32.4ml) 19.8ml


_____5.681g_____ = 5.681g (4 sig figs)(52.15ml - 32.4ml) 19.8ml (3 sig figs)



_____5.681g_____ = 5.681g (4 sig figs)(52.15ml - 32.4ml) 19.8ml (3 sig figs)

ANSWER: 0.287g/ml


Mixed Operations and Significant Figures

• What is the result (to the correct number of significant figures) of the following calculations? Assume all numbers are measured.

(179.8) x (24.4 - 23.1)

Scientific Notation

Scientific 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• Of a large number such as

2 500 000 s is written as:

2.5 x 106 s

Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings

2.2 Scientific Notation• A number in scientific notation contains a coefficient (1 or greater, less than 10) and a power of 10.

150 0.000735 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

Comparing Numbers in Standard and Scientific Notation

Standard Format Scientific NotationDiameter of Earth

12 800 000 m 1.28 x 107 mMass of a human

68 kg 6.8 x 101 kgLength of a pox virus

0.000 03 cm 3 x 10-5 cm

Comparing Numbers in Standard and Scientific Notation

Standard Format Scientific NotationDiameter of Earth

12 800 000 m 1.28 x 107 m (3 sig figs)Mass of a human

68 kg 6.8 x 101 kg (2 sig figs)Length of a pox virus

0.000 03 cm 3 x 10-5 cm (1 sig fig)

NOTE: The Coefficient is used to identify the number of significant figures in the measurement.

Dimensional Analysis

Defining Conversion Factors

Conversion Factors• Conversion factors

– A ratio that specifies how one unit of measurement is related to another

• Creating conversion factors from equalities– 12 in.= 1 ft

– I L = 1000 mL

1 = in 12

ft 1or 1

ft 1

in 12

1 = L 1

mL 1000or 1

mL 1000

L 1


How many seconds are in 2 minutes?

2 minutes x 60 seconds =

1 minute

120 seconds (exactly)


If we assume there are exactly 365 days in a year, how many seconds are in one year?


• A problem solving method in which the units (associated with numbers) are used as a guide in setting up the calculations.

unitsdesiredinAnswerunitgiven

unitdesiredxunitgivenintMeasuremen

Conversion Factor

Exact vs Measured Relationships

• Metric to Metric – exact

• English to English – exact

• Metric to English – typically measured

(must consider sig figs)

English to Metric Conversion Factors


What is 165 lb in kg?

STEP 1 Given: 165 lb Need: kg

STEP 2 Plan

STEP 3 Equalities/Factors

1 kg = 2.205 lb

2.205 lb and 1 kg

1 kg 2.205 lb

STEP 4 Set Up Problem

Practice Problem

• On a recent trip to Ireland, my average cost per day was 250. Euro. What was my average cost in U.S. Dollars?

(1 Euro = 1.36 U.S. Dollars)

50

A rattlesnake is 2.44 m long. How many centimeters long is the snake?

A) 2440 cm

B) 244 cm

C) 24.4 cm

Learning Check

Learning Check

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

(1000mm = 1m, 12 inches=1ft, 1m=39.37inches)

A. 0.910 mm

B. 91 mm

C. 910 mm

chemistry 103 lecture 2. outline i. sig figs – identification – rounding – math operations ii....

Documents

sig figs identification

significant zeros

precision slide

calculation slide

number of significant

significant figures

benjamin cummings slide

fewer significant digits