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Lesson Content

Scientific notation is a special type of exponential notation that allows scientists to express very large or very small numbers. For example, 6.022 x 10²³ is a common number used in chemistry.

There are three parts to the number: coefficient, base, and exponent.

Coefficient

The coefficient is the number before the base of 10. Two other important names for the coefficient are the mantissa and significand.

The coefficient is the first difference between scientific notation and exponential notation. In exponential notation, the coefficient may be any number. However, in scientific notation, the coefficient must be greater than 1 and less than 10.

Base

Scientific notation is extremely useful to scientists because the numbers remain in base 10. This is the number of fingers or toes most human beings have on their bodies - and makes counting very easy. In contrast, computers use binary digits (two, think of bits for computers) or hexadecimal (hex or base 16).

Exponent

The exponent is to the right of the base and raised above the base. A positive exponent means the number is greater than 1, while a negative exponent means the number is less than 1.

Examples

Compare the first number below as written in exponential notation and the second number is written in scientific notation. Both are equal to each other. The difference is the coefficient.

12 x 10⁵ = 1.2 x 10⁶

Writing Scientific Notation

Changing a number from standard notation to scientific notation is very easy. Many students confuse the left or right movement for the exponent - and choose the wrong charge (positive or negative) and so there is an easier way to get the correct answer.

Sample Problem

Let's convert 1200000 to scientific notation.

Step 1. Determine the coefficient. For the number 1200000, the coefficient will be 1.2. This is because 1.2 is between 1 and 10. Do not use 12 or 120 or even .12 for the coefficient.

Step 2. Count the difference in location of the decimal between 1200000 and 1.2. There are 6 place differences between 1200000. and 1.2

This means we have the number 1.2 x 10⁶.

Why do we know the exponent is 6 and not -6? Because the original number is greater than 1, we know the exponent must be a positive number.

Sample Problem

Now, let's convert .0000023 to scientific notation.

Step 1. Determine the coefficient. For the number .0000023, the coefficient will be 2.3. This is because 2.3 is between 1 and 10.

Step 2. Count the difference in location of the decimal between .0000023 and 2.3. There are 6 place differences between the numbers - however this time the original number is less than 1, so we know the exponent is a negative number.

Therefore, the answer is 2.3 x 10^-6.

Alternative Expressions

Exponents may be expressed using other notations. The number 23,000,000,000 can also be written as:

2.3E+10 or as 2.3 X 10^10

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