Multiplying and Dividing
in Scientific Notation
Multiplying Numbers in
Scientific Notation
• Multiply the decimal numbers together.
• Add the exponents to get the power of 10.
• General formula:
(N X 10x) (M X 10y) = (N) (M) X 10x+y
Example 1
• Given:
•
•
•
•
•
3.42 X 105 • 4.67 X 109
Multiply decimals: 3.42 X 4.67 = 15.97
Add Exponents: 105 x 109=105+9=1014
Preliminary Answer: 15.97 X 1014
Now, Rewrite in Scientific Notation if needed.
Final Answer:
1.597 X 1015
Example 2
• Given:
(2.93 X 10-2) • (8.3 X 10-5)
• Multiply Decimals: 2.93 X 8.3 = 24.319
• Add Exponents: 10-2 x 10-5=10-2+(-5)=10-7
• Answer: 24.319 X 10-7
• Rewrite in Scientific Notation
• Final Answer: 2.43 X 10-6
Dividing Numbers in
Scientific Notation
• Divide the decimal numbers.
• Then subtract the exponents
• General formula:
N  10
x
xy
N
  10
y
M
M  10
Example 1
• Given: 8 • 10-3
2 • 10-2
• Divide decimals: 8÷2 = 4
• Subtract exponents: (-3)-(-2)= -1
•
Final Answer:
4 •10-1
Example 2
• Given: 3.45 X 102
1.23 X 10-5
• Divide decimals: 3.45 ÷ 1.23= 2.81
• Subtract exponents: 2- -5 =7
•
Answer: 2.81 X 107
How to do calculations on your scientific calculator
1. Make sure that the number in scientific notation
is put into your calculator correctly.
2. Read the directions for your particular calculator. For
basic scientific
calculators: Punch the number (the decimal number) into your calculator.
Push the EE or EXP button. Do NOT use the x (times) button!!
3. Enter the exponent number. Use the +/- button to change its sign.
Voila!
To check yourself:
multiply 6.0 x 105 times 4.0 x 103 on your calculator.
Your answer should be 2.4 x 109.
Practice Quiz Questions
Question 1
Write these 2 numbers in scientific notation:
0.000467
32000000
Question 2
Express 5.43 x 10-3 in standard form
Question 3
(4.5 x 10-14) x (5.2 x 103) = ?
Question 4
(6.1 x 105)/(1.2 x 10-3) = ?
Question 5
(3.74 x 10-3)4 = ?