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Basic Operations

Basic Operations

Scientific Notation

Scientific notation is an operation using exponents to write very large and very small numbers. Just like exponents, scientific notation was invented so that we don't have to spend wasted time writing out numbers like 25,000,000,000,000,000,000,000,000,000,000,000 (our fingers just cramped typing all those zeros). 

Instead we can write this crazy long number as 2.5 x 10^34

Scientific notation has three parts: to it, the coefficient, base, and exponent

1.23 x 10^4

The coefficient must be greater than 1 and less than 10 and contain all the significant digits in the number. 

  • 12.5 x 10^6 is not in scientific notation, since the coefficient is greater than 10
  • Neither is 0.125 x 10^7, since the coefficient is less than 1

The base is always 10

The exponent is the number of places the decimal was moved to obtain the coefficient.

How to Do It

  1. To get the coefficient, move the decimal to the place after the first "significant digit" in the number. Significant digits are all the non-zero digits in a number. However, if there are zeros in between these numbers, then those zeros are significant, too. Drop all non-significant zeros. We know this sounds confusing. Examples (below) will help, we promise!
     
  2. Multiply that by 10
     
  3. To get the exponent, count the number of places you moved the original decimal. This is your exponent.
     

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