How to Calculate Orders of Magnitude in Exponents

How to Calculate Orders of Magnitude in Exponents thumbnail
How to Calculate Orders of Magnitude in Exponents

Scientific notation is a strategy for writing numbers that are too large or too small to conveniently write in the normal notation. For example, the number 123,000,000,000 converts to 1.23 x 10^11 in scientific notation. The first number of a scientific notation must be between 1 and 10. This number is referred to as the coefficient. The second number, referred to as the base, must always be 10. The base is then raised to a positive or negative exponent. In 1.23 x 10^11, 1.23 is the coefficient and 11 is the exponent.


  1. Converting a Number to Scientific Notation

    • 1

      Place a decimal after the first digit of your number. For example, if your number is 50,000, put the decimal after 5 and write the number as 5.0000. The coefficient is 5.00.

    • 2

      Count the number of digits from the decimal to the end. In 5.0000, there are four digits. The exponent is 4.

    • 3

      Write the number in scientific notation: coefficient x 10^exponent. In our example, 50,000 translates to 5.00 x 10^4.

    Converting Scientific Notation to a Number

    • 4

      Determine whether you have a positive or negative exponent. For example, 10^-3 is a negative exponent.

    • 5

      Move the decimal the number of places equal to the value of the exponent, adding zeros if necessary. If the exponent is positive, move the decimal place right. A negative exponent shifts the decimal place to the left.

    • 6

      Move the decimal place three steps to the left if you have 7.8 x 10^-3, forming .0078.

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