SCIENTIFIC NOTATION
Unit 1, Concept 6
Materials


Scientific Notation POGIL printouts (3 teams work)
Scientific Notation Practice worksheet (1 per
student)
Key Ideas

Rules of Significant figures
 Rules
of 0’s
 Addition/subtraction
 Multiplication/division

CLO: I can do arithmetic operations and report the
results to the correct number of significant figures
using a POGIL activity and independent practice
Do Now

Calculate the density of a silver statue with
a mass of 105 g, and a volume of 10 cm3.
Do Now

Calculate the density of a silver statue with
a mass of 105 g, and a volume of 10 cm3.
Density =
mass/volume
= 105 g/10 cm3
= 10.5 g/cm3
Objective

I can do arithmetic operations and report
the results to the correct number of
significant figures using a POGIL activity
and independent practice
Homework

Complete the Significant Figures
Practice Worksheet. Due
Thursday/Friday
Agenda
Do Now, Objective (7 min)
 Accuracy and Precision (10 min)
 Introduction to Significant Figures (10
min)
 Team Activity: POGIL (40 min)
 Significant Figures Review (15 min)
 Exit Ticket (5 min)

Agenda
Do Now, Objective (7 min)
 Accuracy and Precision (10 min)
 Introduction to Significant Figures
 Team Activity: POGIL
 Significant Figures Review
 Exit Ticket

Accuracy vs. Precision

Accuracy refers to how close a
measured value is to the true value.
 are you correct?
Precision refers to how close a series of
measurements are to one another.
 are your measurements the same
every time?

Accuracy vs. Precision
Precise Instrumentation
Less
Precise
More
precise
What makes one piece of lab equipment
more precise than another?
•
A piece of lab equipment is more precise
than another if it has smaller increments
(spaces between numbers)
(Ex: A graduated cylinder with 0.5 mL increments
is more precise than a graduated cylinder with 1
mL increments)
What makes one measurement of more
precise than another?
•
A value with more digits (#’s) is
more precise. (3.52 is more
precise than 3.5)
Accuracy and precision: the target example
Accurate and precise
Accuracy and precision: the target example
Precise, but not accurate
Accuracy and precision: the target example
Neither accurate, nor precise
Accuracy and precision: the target example
Accurate, but not precise
Agenda
Do Now, Objective (7 min)
 Accuracy and Precision
 Introduction to Significant Figures (10
min)
 Team Activity: POGIL
 Significant Figures Review
 Exit Ticket

Uncertainty and Significant Figures
Every measurement is an estimate of the
actual value because every measurement
contains a degree of uncertainty or error.
 Error does not mean “mistake”.
 Error (uncertainty) is the variance between
individual measurements that happens
when repeated measurements are made
on the same sample or object.

Uncertainty

Example: four students weighed a dime ($0.10)
multiple times using different types of balances.
The measurements in Set I contain two digits. The first digit (the one’s
place) is called the reproducible digit and the second digit in the
tenth’s place (0.1) is called the doubtful digit.
Agenda
Do Now, Objective (7 min)
 Accuracy and Precision
 Introduction to Significant Figures
 Partner Activity: POGIL (40 min)
 Significant Figures Review
 Exit Ticket

Introduction to POGIL
Today we will be doing our first POGIL activity
 You will be working in groups of 3 to facilitate
your own learning around significant figures

In a POGIL activity, you will look at data to
come to your own understanding of a concept
 You and your group members will figure out
the answers for yourselves, and be able to
explain it to Ms. B!

POGIL

POGIL Group Roles
Reader: you will read all information
aloud
Facilitator: you will lead your group in
discussion for each question/task
Recorder: you will write down all
important information, and answers to
questions
POGIL: Significant Figures


Complete parts B, C, and D of your POGIL
activity sheet
By the end of this activity you will understand
 Uncertainty
 Significant Figures
 Rounding with Sig Figs
 Calculations with Sig Figs
Part B - Uncertainty

An increase in precision DECREASES
uncertainty
Part C – Significant Figures

Non-zero numbers are ALWAYS significant

Rules of Zeros
 Zeros
between non-zeros are ALWAYS significant
 Zeros in the coefficient of scientific notation are ALWAYS
significant
 Zeros after a decimal point are ALWAYS significant
 Trailing
0’s are not significant
 Leading 0’s are not significant
Part D – Rounding & Calculations with
Significant Figures
Rules of Significant Figures
1.
When multiplying/dividing measurements,
the answer must contain the same number
of Sig Figs as the measurement with the
least Sig Figs
108.4 mi/3.5 gal = 30.97142857 mpg
= 31 mpg
Rules of Significant Figures
2.
When adding/subtracting measurements,
the answer must contain the same number
of decimal places as the starting
measurement with the least amount of
decimal places.
7.6 mL + 125 mL = 132.6 mL
= 133 mL
Agenda
Do Now, Objective (7 min)
 Accuracy and Precision
 Introduction to Significant Figures
 Partner Activity: POGIL
 Significant Figures Review
 Exit Ticket (5 min)

Exit Ticket


Complete the Exit Ticket at your desk, and
hand it to Ms. Bergman as you leave class.
NO calculators!
45 Minute Version of Lesson

No POGIL
Materials


Scientific Notation Practice worksheet (1 per
student)
Exit Ticket (1 per student)
Key Ideas

Rules of Significant figures
 Rules
of 0’s
 Addition/subtraction
 Multiplication/division

CLO: I can do arithmetic operations and report the
results to the correct number of significant figures
using a notes and independent practice
Do Now

Calculate the density of a silver statue with
a mass of 105 g, and a volume of 10 cm3.
Do Now

Calculate the density of a silver statue with
a mass of 105 g, and a volume of 10 cm3.
Density =
mass/volume
= 105 g/10 cm3
= 10.5 g/cm3
Objective

I can do arithmetic operations and report
the results to the correct number of
significant figures using notes and
independent practice
Homework

Complete the Significant Figures
Practice Worksheet. Due
Thursday/Friday
Agenda
Do Now, Objective (7 min)
 Accuracy and Precision (7 min)
 Uncertainty (5 min)
 Significant Figures (10 min)
 Independent Practice (10 min)
 Exit Ticket (3 min)

Accuracy vs. Precision


Accuracy refers to how close a
measured value is to the true value
Precision refers to how close a series
of measurements are to one another.
Accuracy vs. Precision
Accuracy and precision: the target example
Accurate and precise
Accuracy and precision: the target example
Precise, but not accurate
Accuracy and precision: the target example
Neither accurate, nor precise
Accuracy and precision: the target example
Accurate, but not precise
Precise Instrumentation
• lab equipment is
more precise when
it has smaller
increments (spaces
between numbers)
(Ex: A graduated cylinder with 1
mL increments is more precise than
a graduated cylinder with 10 mL
increments)
More
precise
Less
Precise
Precise Measurements
•
Numbers with more digits (places)
are more precise.
•
•
3.52 is more precise than 3.5
2.14 is more precise than 2.1
Agenda
Do Now, Objective (7 min)
 Accuracy and Precision (7 min)
 Uncertainty (5 min)
 Significant Figures (10 min)
 Independent Practice (10 min)
 Exit Ticket (3 min)

Uncertainty and Significant Figures


Measurements have uncertainty because
you never know the EXACT value
Uncertainty is the variance between
individual measurements that happens
when repeated measurements are made
on the same sample or object.
Uncertainty
The pencil is between 25.5 and 26.0 cm long. The uncertainty is ±0.1 cm
Agenda
Do Now, Objective (7 min)
 Accuracy and Precision (7 min)
 Uncertainty (5 min)
 Significant Figures (10 min)
 Independent Practice (10 min)
 Exit Ticket (3 min)

Significant Figures
Significant figures are those numbers in a
measurement that are known with
CERTAINTY
 They matter

Significant Figures

Four students weighed a dime ($0.10) multiple times
using different types of electronic balances.
The measurements in Set I contains two digits.
• The first digit (the one’s place) is called the reproducible digit
• The second digit in the tenth’s place (0.1) is called the doubtful
digit.
Significant Figures
•
Reproducible Digit: a number that can be reproduced in
multiple measurements. All digits that can be reproduced.
•
Doubtful Digit: a number that cannot be reproduced in
multiple measurements. The last digit in the measurement.
Significant Figures
Sig Fig Rules

1.
2.
3.


Non-zero numbers are ALWAYS significant
Rules of Zeros
Zeros between non-zeros are ALWAYS significant
Zeros in the coefficient of scientific notation are
ALWAYS significant
Zeros after a decimal point are ALWAYS
significant
Trailing 0’s are not significant
Leading 0’s are not significant
Sig Fig Examples

Non-zero numbers are ALWAYS significant
 234
= 3 sig figs
 3 = 1 sig fig
 5426 = 4 sig figs

Zeros between non-zeros are ALWAYS significant



80.3 = 3 sig figs
3017 = 4 sig figs
Zeros in the coefficient of scientific notation are
ALWAYS significant


3.008 x 106 = 4 sig figs
7.20 x 102 = 3 sig figs
Sig Fig Examples Continued…

Zeros after a decimal point are ALWAYS
significant



Trailing 0’s are not significant



2.0 = 2 sig figs
3.420 = 4 sig figs
700 = 1 sig fig
70180 = 4 sig figs
Leading 0’s are not significant


0.0034 = 2 sig figs
0.09 = 1 sig fig
Multiplying & Dividing Sig Figs
1.
When multiplying/dividing measurements,
the answer must contain the same number
of Sig Figs as the measurement with the
least Sig Figs
108.4 mi/3.5 gal = 30.97142857 mpg
= 31 mpg
Adding & Subtracting with Sig Figs
2.
When adding/subtracting measurements,
the answer must contain the same number
of decimal places as the starting
measurement with the least amount of
decimal places.
7.6 mL + 125 mL = 132.6 mL
= 133 mL
Sig Fig Independent Practice

Get started on your Sig Fig Practice
Worksheet
 1.
– a, c, e, g, i, k, m, o
 2. – a, c, e
 3. – a, c
 4. – a, c, e, g
 5. a, c, e
 6. entire problem
Exit Ticket


Complete the Exit Ticket at your desk, and
hand it to Ms. Bergman as you leave class.
NO calculators!