Scientific Notation with a Calculator

Key Questions

  • How do you multiply expressions written in scientific notation?

    Expressions can be easily multiplied when written in scientific notation by:
    1. First, multiplying the numbers other than the powers of 10.
    2. Second, multiplying the powers of 10
    And then, writing them as a product.

    Let us take the general case first.

    Multiplying two numbers #x*10^m# and #y*10^n#

    First, multiplying the numbers other than the powers of 10, we get:
    #x*y=xy#

    Second, multiplying the powers of 10 we get
    #10^m*10^n=10^(m+n)#

    And then writing them as a product, we get
    #xy*10^(m+n)#

    Therefore, #(x*10^m)*(y*10^n)=xy*10^(m+n)#

    Note: When the bases of 2 numbers are equal, their powers can be added up!
    Examples:
    1). #2^a*2^b=2^(a+b)#
    2) #3^3*3^7=3^(3+7)=3^10#

    Now, let's take some specific examples.

    Q: Multiply #1.2*10^3# and #2.3*10^4#

    A:

    #(1.2*10^3)*(2.3*10^4)#
    #=(1.2*2.3)*(10^(3+4))#
    #=2.76*10^7#

    Q: Multiply #9.32*10^21# and #8.21*10^32#

    A:

    #(9.32*10^21)*(8.21*10^32)#
    #=(9.32*8.21)*(10^(21+32))#
    #=76.5172*10^53#

    Notice that this answer is not in the standard form. So, converting this into standard form, we get:

    #=7.65172*10^54#

    Tanish J. · 1 · Nov 29 2014
  • How do you use the calculator to check your answers of expressions written in scientific notation?

    Answer:

    Depends on the kind of calculator you're using..

    Explanation:

    But mostly you have to switch your Calculator to ENG MODE

    For it to be displaying answers in Scientific Notation.

    Jumbotron · 1 · Jul 31 2018

Questions

Exponents and Exponential Functions