Objectives
After completing the Part II (of 2) scientific notation online lab
exercises, students will be able to manipulate and interpret large
numbers expressed in the "mantissa and exponent" format of scientific
notation.
Preliminary Knowledge
 Basic math skills.
 Basic familiarity with webbrowser navigation.
 Students should have completed the ASPIRE lab
"Scientific Notation I: The Exponent" or its equivalent.
Materials
 Computer Lab with Internet connection or a single machine and
suitable projection equipment. We recommend a Pentium class
or Mac OS 8.6 G3 (or later) computer (166 MHz, with at least
32 MB RAM).
 Javacapable and enabled browser with the Java RunTime
Environment plugin installed. For questions/assistance write
support@cosmic.utah.edu .
 Student Lab Packet  This is a printable version
of the lab materials (instructions, frequent questions, graph
formats, and questions/problems) where students can record their
lab data.
Invitation to Learn
 Have students mathematically manipulate some large numbers,
for example of the sort that appear in population graphs.
Multiply 6 billion (the number of people in the world)
by the number of eyes/fingers/teeth/cells in the human body.
Have them do these calculations using conventional
notation.
 Ask the students to identify the difficulties in
these manipulations, and to suggest alternative ways to
perform these operations beyond the standard techniques for
multiplication, division, et cetera that they are
familiar with. Can they arrive at a scheme similar to
the standard scientific notation?
Lab Procedure
PreAssessment: To quickly gauge your students' present (if any)
understanding of "scientific notation", you may have them connnect
scientific and conventional notation by filling out "blanks" in
a table such as that below.
English

Conventional Notation

Scientific Notation

One

1

1 x 10^{0}

Ten

10

1 x 10^{1}

Hundred

100

1 x 10^{2}

Thousand

1,000

1 x 10^{3}

Million

1,000,000

1 x 10^{6}

Billion

1,000,000,000

1 x 10^{9}

et cetera

et cetera

et cetera

DIRECTIONS FOR TEACHING THE LAB
This symbol appears when lab partners are expected to discuss
ideas with each other.
Invite students to proceed to the beginning of the
Student Lab. They should first read the introductory statements and other
information that pertains to the lab. As students scroll down the page,
they will see the lab setup, consisting of three applets:
 "Button Play" applet allows students to relate scientific
and conventional notations.
 A "Do you know it?" applet will randomly generate problems
relating scientific and conventional notations. Students
can record their answers to these questions in logs
included in the student lab packets.
 A "stepthrough" applet guides students through the basics
of multiplication and division of numbers
expressed in scientific notation.
Following these applets students should be drilled on scientific
notation problem solving, for example by solving the problems given
in the accompanying Student Packet. Making use of the applets
should help the students at first, with experience they will ideally
learn to solve the problems independently of the ASPIRE applets.
CLOSURE
SUMMARY: This lesson introduces students to the formalism of
"scientific notation" and to its arithmetical manipulation.
Students should have discovered how to
 Convert a conventional number into scientific notation, and
viceversa.
 Perform the operations of multiplication and
division on numbers expressed in scientific notation.
Having learned these basics, students will then be expected to perform
some basic drills in order to gain proficiency in the formalism.
POSTASSESSMENT: Teachers may return to the preassessment
questions and use these same questions or compose their own postassessment
instrument. Hopefully, teachers can also include more difficult, higherlevel
questions in their postassessment.
EXTENSION ACTIVITIES: In addition to the problems and questions given
at the end of the lab activity, more difficult problems can be used to
test their understanding.
