# Division in Scientific Notation

Part 2: How Do we Divide 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 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.

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).

(4 X 106) / (2X104)=

(9 X 108) / (2 X 10 6)=

(3 X 107) / (8 x 104)=

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 1011 = 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.

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

(7 X 10-5 ) / (2 X 10 10)=

(1.5 X 10-7) / (3.0 x 104)=

(3 X 107) / (8 x 10-6) =

Go to Word Problems Using 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.