How to Write Numbers in Scientific Notation

Scientific notation is a standard way of writing very large and very small numbers so that they're easier to both compare and use in computations. To write in scientific notation, follow the form

image0.png

where N is a number between 1 and 10, but not 10 itself, and a is an integer (positive or negative number).

You move the decimal point of a number until the new form is a number from 1 up to 10 (N), and then record the exponent (a) as the number of places the decimal point was moved. Whether the power of 10 is positive or negative depends on whether you move the decimal to the right or to the left. Moving the decimal to the right makes the exponent negative; moving it to the left gives you a positive exponent.

To see an exponent that's positive, write 312,000,000,000 in scientific notation:

  1. Move the decimal place to the left to create a new number from 1 up to 10.

    Where's the decimal point in 312,000,000,000? Because it's a whole number, the decimal point is understood to be at the end of the number: 312,000,000,000.

    So, N = 3.12.

  2. Determine the exponent, which is the number of times you moved the decimal.

    In this example, you moved the decimal 11 times; also, because you moved the decimal to the left, the exponent is positive. Therefore, a = 11, and so you get

    image1.png
  3. Put the number in the correct form for scientific notation

    image2.png

To see an exponent that's negative, write .00000031 in scientific notation.

  1. Move the decimal place to the right to create a new number from 1 up to 10.

    So, N = 3.1.

  2. Determine the exponent, which is the number of times you moved the decimal.

    In this example, you moved the decimal 7 times; also, because you moved the decimal to the right, the exponent is negative. Therefore, a = –7, and so you get

    image3.png
  3. Put the number in the correct form for scientific notation

    image4.png
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