Scientific Notation Is Simply a Method for Expressing, and Working With, Very Large Or

Scientific Notation Notes

Scientific notation is simply a method for expressing, and working with, very large or very small numbers. It is a short hand method for writing numbers, and an easy method for calculations. Numbers in scientific notation are made up of three parts: the coefficient, the base and the exponent. Observe the example below:

5.67 x 105

This is the scientific notation for the standard number, 567 000. Now look at the number again, with the three parts labeled.
5.67 x 105
coefficient base exponent

In order for a number to be in correct scientific notation, the following conditions must be true:

1. The coefficient must be greater than or equal to 1 and less than 10.
2. The base must be 10.
3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation. A negative exponent means that the decimal is moved to the left when changing to standard notation.

Positive Exponent: actual value more than 10

Negative Exponent: actual value less than 1

Changing numbers from scientific notation to standard notation.

Ex.1 Change 6.03 x 107 to standard notation.

remember,

107 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10 000 000

so, 6.03 x 107 = 6.03 x 10 000 000 = 60 300 000

answer = 60 300 000

Instead of finding the value of the base, we can simply move the decimal seven places to the right because the exponent is 7.

So, 6.03 x 107 = 60 300 000

Now let us try one with a negative exponent.

Ex.2 Change 5.3 x 10-4 to standard notation.

The exponent tells us to move the decimal four places to the left.

so, 5.3 x 10-4 = 0.00053