IESN - Scientific Notation Lesson

Scientific Notation

In this lesson, you will learn how to convert numbers written in standard from into scientific notation and how to convert scientific notation into numbers written in standard form.  Then, you will learn to perform addition, subtraction, multiplication, and division with numbers written in scientific notation.

Scientific Notation is simply shorthand for writing very large or very small numbers. Check out the examples in the table below.

Table of numbers in standard form and scientific notation

Image of a number and the parts of it as it is written in scientific notation

A positive exponent means to move the decimal to the right and a negative exponent means move the decimal to the left.

Image showing how to turn words into a scientific number

Try It

Express each number as scientific notation:

    1. 43,000,000
    2. 604,000,000,000

Express each number as standard notation:

    1. 9.901 x 107
    2. 8.8 x 10-3

Solutions:

  1. Start at the end and move the decimal 7 spaces to the left. 4.3 x 107
  2. Start at the end and move the decimal 11 spaces to the left.  04 x 1011
  3. Start at the 9 and move the decimal 7 spaces to the right. 99,010,000
  4. Start at the 8 and move 3 spaces to the left. 0.0088

Scientific Notation Application

We can perform the operations of addition, subtraction, multiplication, and division with numbers that are in scientific notation.

Rules for these basic operations

Adding and Subtracting Steps

  1. Make any necessary adjustments to the power of 10 so both expressions have the same exponent.
  2. Recall the expression must remain balanced by adjusting the decimal of the coefficient as well. The number of adjustments to the exponents equates to the number of times the decimal must be moved. 
  3. Add or subtract coefficients.
  4. Bring over the common power of 10.
  5. Adjust the expression if not written in proper scientific notation.

Examples of Adding and Subtracting

AddingandSubtractingSNApp.png

Multiplying and Dividing Steps

  1. When multiplying or dividing multiply or divide like “parts” of the expression.
  2. Multiply or divide the coefficients, the first part of the expression.
  3. Multiply or divide the powers of 10, the second part of the expression, by applying the product or quotient rule of exponents learned in the first part of this module.
  4. Adjust the expression if not written in proper scientific notation.

Examples of Multiplying and Dividing

Examples of multiplying and dividing using scientific notation

MUST ADJUST! The third example is not written in proper scientific notation. Recall the coefficient must be 1 or greater but less than 10. The value preceding the decimal must be a single digit. The decimal must be moved one unit left: 24 to 2.4, decreasing this part of the expression by a power of 10.

When adding or subtracting the powers of 10 must be the same. Just as adding and subtracting like terms.

View the Khan Academy videos below to learn more.

 Division in scientific notation is much like multiplication. The difference is that you divide the stems, or coefficients, and subtract the exponents. Remember, when dividing like bases, you subtract the exponents.

Example:
(8 x 106)   = (8)(106) = 2 x 106-3 = 2 x 103
(4 x 103)       (4)(103)

Addition and Subtraction have the same rule, and then you add or subtract depending on the signs. You can only add or subtract like terms, right? That seems to be a recurring theme as we work our way through the course!! The base of ten and its exponent are considered the "term." If you have 103 and 105, those are NOT like terms and you cannot combine those. We can, however, move our decimal point and adjust our exponent so that they are the same. Then, we just combine our stems, or coefficients as dictated by the signs.

This video will show you how to adjust so that you do have like terms. 

Try this matching activity to practice your operations with scientific notation.

It is also important to note how scientific notation looks when using technology. You may have noticed on your calculator that when you are using really large or really small numbers that your calculator's display may not be large enough to house it. You may see something like this 4.87894 E 8 or 4.87894 e+8.

This simply means 4.87894 x 108.

If you saw the following displayed on your calculator screen, what would it mean? Write each in standard notation, then check your answers.

  1. 2.789 E 4
    • Solution: 27,890
  2. 3.59e+5
    • Solution: 359,000
  3. 5.002 E-8
    • Solution: 0.00000005002

Practice

If you would like to practice these types of problems and check your work before you complete your graded homework assignment, click here. Links to an external site.  Make sure you check your answers and look at the course resources or ask your teacher if there are any problems you do not understand. Links to an external site.

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