CP Algebra I
Homework: ________________________________________
7.2 & 7.4 Scientific Notation
Objectives: To write numbers in scientific notation; to re-write scientific notation to number form
To order numbers written in scientific notation; to multiply numbers written in scientific
notation ; to divide numbers in scientific notation
Writing Numbers in Scientific Notation
Example 1) 267,000
Step 1: Determine where the decimal point is in the number
Step 2: Determine where would you put the decimal to make this
number be between 1 and 10
Step 3: Decide how many decimal places you need to move the decimal
Step 4: Write the new decimal × 10𝑛 , 𝑛 = # of places*
*Note: + if the original number is more than 1, the exponent is positive
- if the original number is less than 1, the exponent is negative
Example 2) 4,605,000
Example 3) 0.0000325
Example 4) 0.00000009
Quick Check:
a) 678,000
b) 0.00000435
c) 43,567,800
Rewriting Scientific Notation in “Number Form” (or Standard Form)
Step 1: Move the decimal point to the right for positive exponents of 10.
104
Move the decimal point to the left for negative exponents of 10.
The exponent tells you how many places to move.
Step 2: Fill in with zeros
Example 6) 5.07 × 104
10−6
Example 7) 5.6 × 10−4
Example 5) 3.2 ×
Example 8) 8.3 ×
Quick Check:
d) 4.567 × 105
e) 6.7893 × 10−3
f) 2.45 × 10−5
Using Scientific Notation to Order Numbers
Step 1: Write every number in correct scientific notation
Step 2: Order each by exponent first and then by coefficient
Example 9) Order the numbers from least to greatest: 52 × 104 , 512 × 103 , 5.32 × 102 , 534
Quick Check:
Order the numbers from least to greatest: 60.2 × 10−5, 63 × 104 , 0.067 × 103 , 61 × 10−2
Multiplying a Number in Scientific Notation
Step 1: Multiply the number times the coefficient
Step 2: Simplify so that the number is written in correct scientific notation
Example 10) 2.5(6 × 103 )
Example 11) 5(2 × 10−5 )
Quick Check:
g) 4.2(3 × 10−4 )
h) 5.3(3 × 105 )
Multiplying with Scientific Notation
You can use the property for multiplying powers with the same base to multiply two numbers
written in scientific notation.
Step 1: Multiply the coefficients
Step 2: Add the exponents
Step 3: Make sure your final answer is written in proper scientific notation
Example 12) (6 × 108 )(6 × 10−4 )
10−5 )
Example 13) (5.6 × 10−3 )(3 ×
Quick Check:
i) (4.5 × 104 )(2.3 × 10−3 )
j) (7.23 × 10−2 )(4 × 105 )
Dividing Numbers in Scientific Notation
You can use the property for dividing powers with the same base to divide two numbers
written in scientific notation.
Step 1: Divide the coefficients
Step 2: Subtract the exponents
Step 3: Make sure your final answer is written in proper scientific notation
2.6×105
Example 14) 1.3×10−8
4.2×107
Example 15) 7×10−4
Quick Check:
5.6×102
k) 8×10−3
8.1×104
l) 9×10−3