Scientific Notation II: The Mantissa

Teacher Lesson Plan


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
  1. Basic math skills.
  2. Basic familiarity with web--browser navigation.
  3. Students should have completed the ASPIRE lab "Scientific Notation I: The Exponent" or its equivalent.
  1. 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).
  2. Java-capable and enabled browser with the Java Run-Time Environment plug-in installed. For questions/assistance write .
  3. 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
  1. 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.
  2. 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

Pre-Assessment: 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.

Conventional Notation
Scientific Notation
1 x 100
1 x 101
1 x 102
1 x 103
1 x 106
1 x 109
et cetera
et cetera
et cetera


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:

  1. "Button Play" applet allows students to relate scientific and conventional notations.
  2. 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.
  3. A "step-through" 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.


SUMMARY: This lesson introduces students to the formalism of "scientific notation" and to its arithmetical manipulation.

Students should have discovered how to

  1. Convert a conventional number into scientific notation, and vice-versa.
  2. 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.

POST-ASSESSMENT: Teachers may return to the pre-assessment questions and use these same questions or compose their own post-assessment instrument. Hopefully, teachers can also include more difficult, higher-level questions in their post-assessment.

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.

Back to main Scientific Notation Page

Last Updated: 9 August 2000 by MM