# Multiplication in Scientific Notation

Part 1: How Do we Multiply numbers in Scientific Notation?

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 Multiplication in Scientific Notation:

1) Multiply the coefficients

2) Add the exponents (base 10 remains)

Example 1: (3 x 104)(2x 105) = 6 x 109

What happens if the coefficient is more than 10 when using scientific notation?

Example 2: (5 x 10 3) (6x 103) = 30. x 106

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

30.x106 = 3.0 x 107 in scientific notation.

Example 3:

(2.2 x 10 4)(7.1x 10 5) = 15.62 x 10 9 = 1.562 x 10 10

Example 4:

(7 x 104)(5 x 106)(3 x 102) = 105. x 10 12 --now the decimal must be moved two places over and the exponent is raised by 2. Therefore the value in scientific notation is: 1.05 x 10 14

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).

(2 X 103)(4X104)=

(6 X 105 )(7 X 10 6)=

(5.5 X 107)(4.2 x 104)=

What happens when the exponent(s) are negative?

We still add the exponents, but use the rules of addition of signed numbers.

Example 5: (3 x 10 -3) (3x 10-3) = 9. x 10-6

Example 6: (2 x 10 -3) (3x 108) = 6. x 105

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). Multiply the following:

(3 X 10-6)(2X10-4)=

(5 X 10-5 )(7 X 10 10)=

(5.5 X 10-7)(4.2 x 104)=

(5 X 107)(8 x 10-6)(4.2 x 104)=

Go to Division in Scientific Notation

#### 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.