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 Scientific Notation The Basics

What is Scientific Notation?

Scientific Notation is a method of writing very large or very small numbers in a form of shorthand. Scientists developed this method many years ago to provide them with a method to save time by easily representing numbers by using less characters. The system is based on the powers of Base Ten. Scientific notation provides a place to hold the zeroes that come after a whole number or before a fraction.

You can convert a number to scientific notation by increasing the power of ten by one for each place the decimal point is moved to the left. See the examples below.

Scientific Notation Examples:

Fraction = 1/100
Decimal = 0.01
Scientific Notation = 10-2
(Note: the raised -2 is called the exponent.)

Fraction = 1/10
Decimal = 0.1
Scientific Notation = 10-1

Number = 1
Scientific Notation = 100

Number = 10
Scientific Notation = 101

Number = 100
Scientific Notation = 102

Number = 1000
Scientific Notation = 103

Although one often thinks of 0 as having nothing. Think of the 0 in terms of money. Would you sooner have \$10 or \$100? You can see how important adding a 0 is.

Decimals and Scientific Notation:

Earlier we stated that Scientific Notation is used to represent large or small numbers. The number shown below has one digit to the left of the decimal point. The power of ten (exponent) will show you how many places the decimal point moves.

The number 8.2x10-6 written in decimal format would be 0.0000082 because the decimal point was moved 6 places to the left to form the decimal 0.0000082.

5.63x10-5 represented in decimal notation is 0.0000563 Note: The decimal point was moved 5 places.

4.11 x 10-6 = 0.00000411

Inexact Powers of Ten Examples:

2000 = 2x 1000 = 2 x 103

631,000,000 = 6.31 x 108

Try the online calculator for calculating exponents involving multiplication.

Deb Russell
Mathematics Guide

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