Scientific Notation is based on powers of the base number 10.

The number 123,000,000,000 in scientific notation is written as :

The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10.

*The second number is called the base* . It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten.

Rules for Division in Scientific Notation:

1) Divide the coefficients

2) Subtract the exponents (base 10 remains)

Example 1: (6 x 106) / (2 x 103) = **3 x 103**

__What happens if the coefficient is less than 10? __

Example 2: (2 x 10 7) / (8 x 103) = 0**.**25 x 104

While the value is correct it is __not correctly written in scientific notation__ since the coefficient is not between 1 and 10. We must move the decimal point over to the right until the coefficient is between 1 and 10. For each place we move the decimal over the exponent will be lowered 1 power of ten.

0.25x10 4 = __2.5 x 103__ in scientific notation.

(write
your answers in the form of coefficientx10^exponent) If your answer is 3.5 x 10^{
3 } you should type **3.5x10^3** in the box then click the submit
button).

__What happens when the exponent(s) are negative?__

We still subtract the exponents (apply the rules for subtracting signed numbers)

Example
5: (9 x 10 ^{-6}) / (3x 10^{-3}) = 3. x 10^{-3}

Example
6: (2 x 10 ^{3}) / (4 x 10^{-8}) = 0.5 x 10^{11 }= 5 x
10^{ 10}

**Now
Try these:**

(write
your answers in the form of coefficientx10^exponent) If your answer is 3.5 x 10^{
3 } you should type **3.5x10^3** in the box then click the submit
button). Divide the following numbers using Scientific Notation.

Introduction to Scientiic Notation: Learn the basic principles of scientific notation. Convert standard numbers to scientific notation.

Scientific Notation Generator: Javascript program will enable you to practice converting any number from basic notation to scientific notation.

Multiplication with Scientific Notation: Learn multiplication using scientific notation, with positive and negative exponents.

Division with Scientific Notation: Learn division using scientific notation with positive and negative exponents.

Word Problems using Scientific Notation: Mixed multiplication/division problems, word problems using scientific notation.

An Integrated Math Science and Art (STEAM) Activity- Mass, Volume Density Activity using the Gates Project from Central Park NYC.