Drexel-SDP GK-12 ACTIVITY
Scientific Notation
Subject Area(s)
Math, Science
Associated Unit: N/A
Associated Lesson: N/A
Activity Title : Scientific Notation
Grade Level 8
Activity Dependency Knowledge of addition, subtraction
Time Required 60 minutes
Group Size 1
Expendable Cost per Group: $0
Summary: The goal of this activity is to teach students about the concept of scientific
notation. The activity teaches the concept of moving from standard form to scientific
notation and in addition shows how to move backwards from scientific notation to
standard form.
Engineering Connection: Engineers are constantly using scientific notation in their
research. The idea of expressing very large or very small numbers in a short form to
save time and keep numbers from being misconstrued is crucial to communication in
engineering. Engineers study many large things such as bridges and space and also
very small things such as DNA and viruses. Having ways to expresses the sizes of
these types of things without the use of numerous zeros is crucial.
Keywords: math, scienfic notation,
Educational Standards
• Pennsylvania State Math: 2.1.8A, 2.1.8B, 2.1.8C
Pre-Requisite Knowledge:
• Ability to add and subtract.
Learning Objectives
After this lesson, students should be able to:
• Convert numbers from standard form to scientific notation
•
Convert numbers from scientific notation to standard form
•
Order numbers from smallest to largest when the set of numbers is partially in standard form
and partially in scientific notation
Materials List
Each group needs:
• One index card
•
Notebook
Introduction / Motivation
Scientific Notation is a way of writing numbers that are extremely large or extremely small and
thus have a large number of decimal places or zeros. Engineers love notation like this because it
is efficient (less writing for us) and very clear when discussing things with other engineers. In
the case of very large and very small numbers missing a zero can greatly change a calculation
and that could be a very important calculation that could mean the difference between a space
ship getting safely into space or not. Scientific notation can reduce human error by making
really big or small numbers easier to write and understand.
Engineers are constantly looking at very large and very small things from planets in space to
DNA and bacteria which are too small to see with the human eye. New technology is being
developed at the nano-scale (that means really small) and thus it is becoming more and more
important to use scientific notation when discussing these types of technologies and items.
Vocabulary / Definitions
Word
Definition
Standard
A traditional way of writing numbers including many zeros for very large or very
Notation
small numbers
Scientific
A short hand way of writing numbers that includes two parts: a number between
Notation
1 and 10 and a power of 10 by which the coefficient is multiplied.
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Exponent
A number indicating how many times a base number is used in a multiplication.
It is written with a small number to the upper right of the base number that is
used in the multiplication.
Procedure
Background
Scientific notation is an important tool that scientists and engineers use to describe very large
numbers. For example the speed of light is 300,000,000 m/sec and that is a quantity engineers
use a great deal to describe how light moves and reacts with objects. That number has a whole
lot of zeros in that form and that means a ton of writing. Another object that scientists and
engineers study a great deal are viruses. Viruses can be as small as 0.000000020 meters in
diameter. That is a ton of zeros to write each time we are describing the size of a virus.
Instead of writing a bunch of zeros to describe larger or small objects engineers write things in
scientific notation. Forming a number in scientific notation has 3 easy steps:
1. Place a decimal point in the original number so that there is one, nonzero number to the
left of it. That number should be between 1 and 10.
2. Count the number of places the decimal point was “moved” from its original spot. This
is the exponent of 10.
3. If your original number was less than 1 the exponent of 10 will be negative, otherwise the
exponent is positive.
Lets look at our two example numbers from before. First the speed of light goes from being
written as 300,000,000 m/sec in standard notation to 3 x 108 m/sec. The size of a virus going
from being written as 0.000000020 meters in standard form to 2 x 10-8 meters in scientific
notation.
Now what if we want to move back to standard form? That is even simpler than going to
scientific notation. All we do is move our decimal place the number of times indicated by the
exponent of 10. If the exponent is negative we move the decimal place to the left. If the
exponent is positive we will move our exponent to the left.
Before the Activity
• Have the students give three examples in their notebooks of things that engineers could study
which would be large or small enough to need scientific notation to describe them.
With the Students
1. Review Scientific notation and moving back and forth between that and standard notation.
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2. Give each student an index card with a very large or very small number on it. Make sure
some of the cards have the numbers written in scientific notation and others in standard
notation.
3. Have the students as a class arrange themselves from smallest to largest based on the
numbers on their cards. Do not allow the use of a calculator for this. This will reinforce the
idea of converting between scientific notation and standard form which will be more
comfortable to the students at first.
Safety Issues
• None
Troubleshooting Tips
• Some students may get stuck if you use negative numbers. Remind them of the number line
and ask them if a negative number is smaller or larger than the smallest positive number they
can think of.
Investigating Questions
1. Describe the two parts of a number in scientific notation in your own words.
2. Can you think of 3 things you use every day that could be described with scientific
notation?
Assessment
Pre-Activity Assessment
Students should describe things in their notebook which we would need scientific notation to
describe such as planets, distances of stars, DNA and viruses.
Activity Embedded Assessment
The students should do the card activity and if they convert any numbers they should show all of
their work on a sheet of paper.
Post-Activity Assessment
Students should answer the investigation questions and turn in their responses in full sentence
form.
Activity Extensions
• Ask all students with numbers larger than 1 to move to one side of the classroom and the rest
of the students to move to the other side. Are negative numbers larger or smaller than 1?
This may trip up the students without as much practice dealing with negatives.
• Have a group of students with cards stand up in the front of the room and have another
student place themselves in the correct location in the line. Alternatively place yourself in
the number line created by the smaller group and ask the class if you are in the correct
location.
• A second set of cards can be made that mirrors the first except the notation used (scientific or
standard) is switched. You can then have the students match themselves up with the student
holding the card with the same number but in different notation
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Activity Scaling
• Younger students should be able to do this but may need a great deal more practice simply
converting between standard notation and scientific notation before they can do the ordering
activity.
• Older students can use the card activity as a refresher before an example or standardized test.
Owner
Drexel University GK-12 Program
Contributors
Elaine Garbarine
Copyright
Copyright 2007 Drexel University GK12 Program. Reproduction permission is granted for nonprofit educational use
Version: Mar 2007
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