1. OPERATIONS WITH SCIENTIFIC NOTATION
Essential Question?
How do you add, subtract, multiply, and divide using scientific notation?
8.EE.4

2. Adding & Subtracting with Scientific Notation
One way of adding/subtracting numbers that are written in scientific notation is to write them in standard form, line up the decimals, add/subtract in the traditional manner, then write the answer using scientific notation.
Example: 2.73× × 10 3
273,000
+1,800
274,800
2.748× 10 5

3. Adding & Subtracting with Scientific Notation
The second way is to transform all of the powers of 10 to be the same.
Example: 8.3× × 10 7
Step 1: Rewrite each number with the same power of 10.
0.83× 10 7
Step 2: Add/subtract the multipliers
Step 3: Rewrite in scientific notation:
10.37× 10 7
1.037× 10 8
NOT SCIENTIFIC NOTATION

4. Adding & Subtracting with Scientific Notation
Example: 9.67× 10 −3 −1.3× 10 −5
Step 1: Rewrite each number with the same power of 10.
967× 10 −5
Step 2: Add/subtract the multipliers
Step 3: Rewrite in scientific notation:
965.7× 10 −5
9.657× 10 −3
NOT SCIENTIFIC NOTATION

5. Try These
3.1× × × 10 7

6. Try These
4.3× 10 − × 10 −5 −8.27× 10 −2

7. Adding & Subtracting with Scientific Notation
What must you do when your answer shows a multiplier less than 1 or greater than 10?
Leave it alone.
Move the decimal and change the exponent to make it scientific notation.
Move only the decimal so it looks like scientific notation.
Panic, cry, and tear up the paper.
Is there a method you can think of to correctly move the decimal and change the exponent?

8. Multiplying & Dividing with Scientific Notation
Example: (2.73× 10 5 )(3.35× 10 7 )
Step 1: Multiply/Divide the multipliers.
(2.73)(3.13)
9.1455
Step 2: Use exponents rules for the powers of 10.
=10 12
Step 3: Rewrite in scientific notation:
9.1455× 10 12

9. Multiplying & Dividing with Scientific Notation
Example: (1.4× 10 3 )÷(5.6× 10 6 )
Step 1: Multiply/Divide the multipliers.
(1.4)÷(5.6)
0.25
Step 2: Use exponents rules for the powers of 10.
10 3 ÷ 10 6
10 3−6 = 10 −3
Step 3: Rewrite in scientific notation:
0.25× 10 −3
2.5× 10 −4
NOT SCIENTIFIC NOTATION

10. Scientific Notation on a Calculator
Take out your cell phones and open the calculator app. Use the calculator to multiply the following. 153,000,000,000,000 1,160,000,000 You should get E+23 What do you think this means? × 10 23

11. Scientific Notation on a Calculator
Try this one: