SCIENTIFIC NOTATION

Small to Scientific

Concept: Scientific Notation is a method used to write very small and very large numbers in an abbreviated way. A number in Scientific Notation is expressed as the product of a number between one and nine and a power of ten.

Steps for Converting Small (Decimal) Standard Notation Numbers

To Scientific Notation Numbers

Step 1 | Move the decimal point to the right past the first non-zero digit. Remember how many digits to the right you moved the decimal point. You will need that number in Step 4.
Step 2 | Drop the zeros. Keep only the non-zero numbers.
Step 3 | Write a multiplication problem using the non-zero number you established in Step 2 for the first number in the problem, and 10 as the second number. Limit the digits of the first number to no more than one whole number and two or three decimals.
Step 4 | Raise the 10 (the second number in the multiplication problem) to a power equal to the number of places the decimal was moved in Step 1. (The exponent on the 10 will be the same number as the number of places the decimal point was moved in Step 1.) The exponent will be a negative digit in this case, because the original number is a decimal number, and we moved the decimal point to the right. A small Standard Notation number has been converted to Scientific Notation.

Example Write 0.0000223 in Scientific Notation.

Step 1 | Move the decimal point to the right past the first non-zero digit. | 0 . 0 0 0 0 2 2 3 2.23
| Remember how many digits to the right you moved the decimal point. You will need that number in Step 4. In this case the number is 5. | 0.0 0 0 0 2.2 3
Step 2 | Drop the zeros. Keep only the non-zero numbers. | 2. 2 3
Step 3 | Write a multiplication problem using the non-zero number you established in Step 2 for the first number in the problem, and 10 as the second number. Limit the digits of the first number to no more than one whole number and two decimals. | 2. 2 3 x 10
Step 4 | Raise the 10 (the second number in the multiplication problem) to a power equal to the number of places the decimal was moved in Step 1. (The exponent on the 10 will be the same number as the number of places the decimal point was moved in Step 1.) | 2. 2 3 x 10 5
| The exponent will be a negative digit in this case, because the original number is a decimal number, and we moved the decimal point to the right. | 2. 2 3 x 10 – 5
| A small Standard Notation number has been converted to Scientific Notation. | In Scientific Notation, 0.0000223 is written 2.23 x 10 – 5