In this lesson we will learn how to convert numbers into scientific notations. Scientific notation is a form of writing or expressing a very large or a very small number. It is composed of a whole number and its exponent.

Example:

• 2 x 10⁸
• 5 x 10^-6
• 6 x 10⁴
• 4 x 10^-8

How to make a very large number into a scientific notation

Sometimes, because numbers are so large, mathematicians use scientific notations to express it simply. This is done to save space and make it convenient for both the reader and author.

It is easy to convert large numbers into scientific notation. Just follow these steps:

1. Always put in mind that any whole number can also be written in a decimal form
   3800000 = 3800000.0
2. Then move the decimal point to the left until you have a number that is between 1 and 10.
   Based from the example number above, moving the decimal point to the left will give 3.8
3. Now, let us count the number of times we have moved the decimal point
   Based again on the above example, you have moved the decimal point 6 places to the left
4. We can now express that we have moved the decimal point 6 places to the left by writing 10⁶
   The scientific notation therefore of 3800000 is 3.8 x 10⁶
   3.8 x 10⁶ = 3.8 x 10 x 10 x 10 x 10 x 10 x 10
   3.8 x 10⁶ = 3800000

Examples:

1.    45600000000
      45600000000 = 45600000000.0
       45600000000 = 4.56 x 10¹⁰
2.    37000
       37000 = 37000.0
      37000 = 3.7 x 10⁴
3.     5600000000
      5600000000 = 5600000000.0
       5600000000 = 5.6 x 10⁹
4.    67980000000
      67980000000 = 67980000000.0
      67980000000 = 6.798 x 10¹⁰
5.    50700000
       50700000 = 50700000.0
      50700000 = 5.07 x 10⁷

How to make a very small number into a scientific notation

Mathematicians and scientists also use scientific notations for very small numbers. This is done to make writing
them easy and convenient.

Converting very small numbers into scientific notation is also simple. Just follow these rules:

0.00000078

• Move the decimal point to the right until you have a number that is between 1 and 10.
  Based from the example number above, moving the decimal point to the left would make it to 7.8
• Now, let us count the number of times we have moved the decimal point
  Based again on the above example, you have moved the decimal point 7 places to the right
• We can now express that we have moved the decimal point 7 places to the right by writing 10^-7

The scientific notation therefore of 0.00000078 is 7.8 x 10^-7

7.8 x 10^-7 = 3.8 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1

7.8 x 10^-7 = 0.00000078

Examples:

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