Summary
In this activity, students have a button, which they will move like a decimal point, so they are actively involved in putting numbers into scientific notation and taking numbers out of scientific notation.
Grade Level
Middle School, High school
NGSS Alignment
This lab will help prepare your students to meet the following science and engineering practices:
- Science and Engineering Practices:
- Using Mathematics and Computational Thinking
Objectives
By the end of this lesson, students should be able to
- put numbers into scientific notation.
- take numbers out of scientific notation.
Chemistry Topics
This lesson supports students’ understanding of
- Scientific notation
Time
Teacher Preparation: 15 minutes
Lesson: 30 minutes
Materials
For each group:
- Button, bead, small paperclip, or other marker (to show where the decimal is located)
- Cards with numbers that will be put into scientific notation
Safety
No safety precautions need to be observed when carrying out this activity.
Teacher Notes
- Prepare cards with numbers that will be expressed in scientific notation for each student (or groups of students) to use. In the two "Number Cards" documents, there are some examples to get you started, but you can add to/change them as you see fit.
- There are two sets of Number Cards included, so if you wanted you could put one set in scientific notation and then use those for the second half of the worksheet when students are going from scientific notation to standard form (just so you have fresh numbers).
- You could make a set of cards and laminate them for use year after year. This would also allow students to use dry erase markers on the cards to show decimal movement, rather than a button.
- Remember, the decimal place will be represented by a button/bead/other small marker (change the wording in the document below as needed), so make sure the cards and numbers are written large enough to account for the size of the marker you'll have the students use. There should be a variety of numbers greater than and less than one.
- You could pair this up with a lesson on significant figures and have students identify how many significant figures are in each number.
- Here is a video that could provide extra support/practice for students if they need more examples: https://www.youtube.com/watch?v=6y35Jlz332M. This could be watched in class or assigned for homework either before or after this activity.
For the Student
Lesson
Scientific notation is used to abbreviate numbers that are quite large or small to make them easier to write. A number in scientific notation will follow the form:
B x 10^{n}
where B is a number that is equal to or greater than 1 and less than 10. The n is a positive or negative whole number. The n cannot have decimals but could be zero.
Expressing a Number in Scientific Notation
Sort the numbers out in front of you making a pile of numbers greater than one and a pile of numbers less than one. Using the stack of numbers that is less than one, take the number that is on top. Place a button on the decimal point. Move the button to the right until it is one place to the right of the first nonzero digit. Count the number of places that you moved the button from its original position. This number is the n value in scientific notation. Make the n value negative because you moved the button to the right. The number to the left of the button and its significant digits to the right of the button becomes the B in scientific notation.
In the table below, write the original number and then the number in scientific notation. Repeat this for all of the other numbers that are less than one.
Original Number | Scientific Notation |
For the numbers that are greater than one, choose the number that is on top of the pile. For a number that is one or greater and doesn’t have an obvious decimal point, the decimal point is located all the way to the right after the last number. Using the number that you chose, place the button where the decimal point is/would be.Move the button left until there is only one nonzero digit to the left of it. Count the number of decimal places that you moved the button from the original position. This value is the n value in scientific notation.It should be positive because you moved the decimal point to the left. The digit to the left of the button and the significant digits to the right of the button become the B value in scientific notation.
In the table below, write the original number and then the number in scientific notation.Repeat this for all of the other numbers larger than one.
Original Number | Scientific Notation |
Now, write the rules for writing number in scientific notation. Make sure you have a rule that explains how to do it for numbers less than AND numbers greater than one.
Taking Numbers Out of Scientific Notation
Go back to the first number that you put into scientific notation that was less than one. Rewrite the number in scientific notation in the table below.For numbers less than one, the exponent again tells you how many places that you have to move the decimal place. But when you take a number out of scientific notation, if it has a negative exponent, you move the decimal to the left that many places and substitute zeros as placeholders but keep all the significant digits.
Rewrite the other numbers less than one that are in scientific notation in the table below, then take the numbers out of scientific notation and write them in standard (normal) notation.
Scientific Notation | Standard Notation |
For numbers that are greater than one, again the exponent tells you how many places to move the decimal point.However, for numbers that are greater than one in scientific notation, the exponent will be positive so you have to move the decimal that many places to the right substituting zeros as placeholders but keeping all the significant digits.
Copy all the numbers greater than one in scientific notation in the table below and then write them in standard notation.
Scientific Notation | Standard Notation |