Transcript Writing Scientific Notation

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.
• Examples
A. 5.89 X 107 m
C. 9.00 X 10-3g
B. 3.0 X 1018 dL
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 enter
you see
Write your answer
2.45exp-4
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
1.47exp7/6.00exp10
Press enter
you see
2.45exp-4
Write 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
7 - 10 = -3
• Subtract the exponents
• 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