Dividing with Scientific Notation

How can we deal with so many zeros?

The mass of one carbon atom =12.01

602,200,000,000,000,000,000,000

Covered in this lesson

• This lesson demonstrates how to divide with scientific notation.

– Scientific notation can be divided easily with or without a calculator when the factors (the number between 1 and 10) and exponents (power of ten) are considered.

Scientific Notation

• All scientific notation is expressed with a factor multiplied by a power of 10.• ExamplesA.5.89 X 107 m B. 3.0 X 1018 dLC. 9.00 X 10-3g D. 7.1 X 10 -

12Mm

Methods of Dividing

• There are at least two methods you can use to divide in scientific notation.–The short hand way using a scientific

calculator.–The long hand way without a scientific

calculator.

Using a Scientific Calculator

• If you are dividing in scientific notation use the following method.–Enter the first number in ( ) divided by

the second number in ( )–Press enter

(Note the power of 10 will be given the symbol exp)

Example: Scientific Calculator

• (1.47 X 107) / (6.00 X 1010) =• Put the first number in ( ) divide by

the second number in ( )It looks like this (1.47*10^7)/(6.00*10^10) Press enteryou see 2.45exp-4Write your answer 2.45 X 10-4

2nd Method Using a Scientific Calculator

• Use the exp key dividing as usual.• Enter the numbers as follows: –first number: factor, exp key, exponent –divide – second number: factor, exp key, exponent– Enter

Example: 2nd Method Scientific Calculator

• (1.47 X 107) / (6.00 X 1010) =• Use the exp key and just divide.It looks like this 1.47exp7/6.00exp10Press enter you see 2.45exp-4Write your answer 2.45 X 10-4

Example: Without Calculator

• Divide the factors• Subtract the power of 10

exponents • Put them together • Change back to scientific

notation.

Without Calculator Example

• (1.47 X 107) / (6.00 X 1010) =• Divide the factors 1.47/6.00 = 0.245 • Subtract the exponents 7 - 10 = -3

• Put them together 0.245 X 10-3 • change back to scientific notation.

= 2.45 X 10-4 the final answer

Practice problems

1. (6.38 X 109) / (7.83 X 105) =

2. (2.038 X 107) / (2.00 X 10-11) =

3. (5.89 X 10-5) / (3.0 X 1010) =

4. (9.00 X 10-8) / (7.1 X 10 -4) =

Answers Practice Problems

1. 8.15 X 103

2. 102 X 106

3. 1.96 X 10-15

4. 1.27 X 10-4