# File ```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
Now, Rewrite in Scientific Notation if needed.
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
• 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&divide;2 = 4
• Subtract exponents: (-3)-(-2)= -1
•
4 •10-1
Example 2
• Given: 3.45 X 102
1.23 X 10-5
• Divide decimals: 3.45 &divide; 1.23= 2.81
• Subtract exponents: 2- -5 =7
•
How to do calculations on your scientific calculator
1. Make sure that the number in scientific notation
is put into your calculator correctly.
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.
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 = ?
```