# Scientific Notation

We use scientific notation when we write very big or very small numbers. Scientific notation is when we write one number followed by the decimal symbol (in South Africa that is a comma) and then the remaining parts of the number. However, as we actually ‘moved’ the decimal symbol of the given number we should multiply the number with a base 10 with its necessary exponent.

In the example of 6820, for scientific notation, we want to have 6,82 multiplied with a base 10 with its necessary exponent. How can we achieve that? To end up with a 6,82 we divided the number by 1000. As we need to keep the value the same, we will immediately multiply with a 1000. Remember, division and multiplication are each other’s opposite operations. So, if I divide by 1000 and then immediately multiply by 1000, I do not change the value of the number.

In the example, I then need to say 6,82 x 1000. But, as stated earlier, for scientific notation, we should write the 1000 as base 10 with its exponents. Thus, the answer will be 6,82 x 103 (10 to the power of 3).

In this video two other more difficult and interesting examples are also discussed. Scientific notation includes exponents and thus we advise you to watch our videos we have on exponents and the laws of exponents.