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Basic Operations

Basic Operations

At a Glance - 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.

Scientific Notation Example 1

Write 26,500,000 in scientific notation.

Note: even if you don't see a decimal at the end of a number, it's there.

Scientific Notation Example 2

Write 307,000 in scientific notation.

This time, there is a zero that is a significant digit. Be sure to include this in the coefficient.

Scientific Notation Example 3

Write 5.072 x 10^8 in standard notation.

If scientific notation is shorthand, then standard notation is longhand. It's the way you normally write numbers.

Scientific Notation Example 4

Write 0.00006009 in scientific notation.

Remember when we told you that you could write very small numbers using scientific notation? Well, here's your big (or really small) chance.

Scientific Notation Example 5

Write 3.801 x 10^-12 in standard notation.

Since the ten is raised to a negative power, you know that you are working with a very small number.

Scientific Notation Exercise 1

Write 20,040,000 in scientific notation.

Scientific Notation Exercise 2

Write 5.34 x 10^9 in standard notation.

Scientific Notation Exercise 3

Write 0.000000107  in scientific notation.

Scientific Notation Exercise 4

Write 9.012 x 10^-6 in standard notation.

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