×

Hello! Socratic's Terms of Service and Privacy Policy have been updated, which will be automatically effective on October 6, 2018. Please contact hello@socratic.com with any questions.

Scientific Notation

Key Questions

  • A number in scientific notation is in the form

    #a * 10^b#

    To convert to a real number, write out #a# then move the decimal point depending on #b#'s sign.

    If #b# is positive, move the decimal point to the right
    If #b# is negative, move the decimal point to the left

    For example,

    #1.23 * 10^5#

    Moving the decimal point 5 places to the right, we have

    #123000#


    #4.56 * 10^-5#

    Moving the decimal point 5 places to the left, we have

    #0.0000456#

  • First, observe what happens when a particular number is multiplied or divided by multiples of 10.


    #123.45 * 10 = 1234.5# Decimal place moved by 1 place to the right

    #123.45 * 100 = 12345# Decimal place moved by 2 places to the right

    #123.45 * 10000 = 1234500# Decimal place moved by 4 places to the right

    #67.89 * 1/10 = 6.789# Decimal place moved by 1 place to the left

    #67.89 * 1/100 = 0.6789# Decimal place moved by 2 places to the left

    #67.89 * 1/10000 = 0.6789# Decimal place moved by 4 places to the left


    Remember that a number's multiples can also be expressed exponential form

    #1 = 10^0#
    #10 = 10^1#
    #100 = 10^2#
    #10000 = 10^4#
    #1/10 = 10^-1#
    #1/100 = 10^-2#
    #1/10000 = 10^-4#


    A number in scientific notation form is in the form

    #A * 10^b#

    where #A# is a rational number in decimal form.

    To convert to a number in scientific notation form,
    move the decimal place by #b# places. If #b# is negative, move to the left. If #b# is positive, move to the right

Questions