1. Operations with Scientific Notation (Part I, II, III, IV)
8th Grade Math
By Mr. Laws

2. Goal/Standards
8.EE.4 – Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation is used.
Interpret scientific notation that has been generated by technology.

3. Essential Question(s):
Using Math Principle, how can I add, subtract, multiply, and divide using scientific notation?
Explain how do I use a scientific or graphing calculator to solve scientific notation problems?

4. Adding and Subtracting in Scientific Notation Part I

5. Addition and Subtraction with Scientific Notation
Rules for adding and subtracting exponents are different from the properties of exponents.
When adding and subtracting in scientific notation, the base 10 exponent must have like terms. (two of the base numbers will have same powers)
Adding and subtracting in scientific notation can be done in scientific notation form or rewriting them in standard form.

6. Adding in Scientific Notation Method 1
Steps
Simplify: (3.5 x 104) + (1.65 x 104)
Step 1: = 5.15
Step 1 – Add the terminating decimals. ( )
Step 2: are like terms
Step 2 – Notice the base/exponents are like terms
Step 3: x 104
Step 3 – Rewrite step 1 and step 2 in scientific notation form.
Note: Always check to see if the decimals following the S.N rule.

7. Adding in Scientific Notation Method 2
Simplify: (7.5 x 105) + (5.20 x 103)
Steps
Step 1: , ,200 =
Step 1 – Change the scientific notations to standard form. Why?
Step 2: ,200
Step 2 – Add them together to get the total number.
Step 3: x 105
Step 3 – Rewrite in scientific notation form.
Note: Always check to see if the decimals following the S.N rule.

8. Subtracting in Scientific Notation Method 1 and 2
Simplify: (8.5 x 105) - (5.2 x 105)
Simplify: (3.5 x 104) - (1.2 x 102)
Step 1: Change scientific notation
to standard form
Step 1: – 5.2 = 3.3
Step 2 : 105 are like terms
Step 2 : – 120 = 34880
Step 3: x 105
Step 3: x 104

9. Scientific Notation with Calculator Part II

10. Scientific Notation with Calculator
Your can enter numbers in scientific notation by using a scientific calculator or graphing calculator (TI.83/84).
Numbers/answers can be displayed in scientific notation form or standard form.
On the TI-83 or TI 84, you will have to type terminating decimal, press the 2nd button, and EE button (comma button).
The letter “E” will be shown on the display screen which takes the place of the base 10, and follow by the power.
Example 1: 4.5E9 = 4.5 x 109

11. Scientific Notation with Calculator
2.94 x 1015
2.) 5.5E-11 =
5.5 x 10-11

12. Multiplying in Scientific Notation Part III

13. Properties of Exponents
When multiplying or dividing numbers written in scientific notation, when can use the properties of exponents to help get the answer. The following are properties we will use:
Multiplication Property of Exponents
When multiplying bases with exponents, you add the exponents.
Dividing Property of Exponents
When dividing bases with exponents, you subtract the exponents.

14. Multiplying in Scientific Notation Example # 1
Steps
Simplify: (2.5 x 104) (3.4 x 102)
Step 1: x 3.4 = 8.5
Step 1 – Multiply the terminating decimals. (2.5 x 3.4)
Step 2: x 102 = 106
Step 2 – Add the exponents of 104 and 102
Step 3 – Rewrite step 1 and step 2 in scientific notation form.
Note: Always check to see if the decimals following the S.N rule.
Step 3: x 106

15. Multiplying in Scientific Notation Example # 2
Steps
Simplify: (4.2 x 109) (5.5 x 102)
Step 1: x 5.5 = 23.1
Step 1 – Multiply the terminating decimals. (4.2 x 5.5 )
Step 2: x 102 = 1011
Step 2 – Add the exponents of 109 and 102
Step 3 – Rewrite step 1 and step 2 in scientific notation form.
Is this answer in S.N form? Explain
Step 3: x 1011
Step 4– Change 23.1 to 2.31 by moving decimal point one place to the left, and add 1 exponent to 1011 to make it 1012
Step 4: x 1012

16. Multiplying in Scientific Notation Example # 3
Steps
Simplify: (7.4 x 10-3) (2.5 x 10-3)
Step 1: x 2.5 = 18.5
Step 1 : Multiply the terminating decimals. (7.4 x 2.5 )
Step 2: x 10-3 = 10-6
Step 2 : Add the exponents of 10-3 and 10-3
Step 3 : Rewrite step 1 and step 2 in scientific notation form.
Is this answer in S.N. form? Explain
Step 3: x 10-6
Step 4: Change 18.5 to 1.85 by moving decimal point one place to the left, and add 1 to 10-6 to make it 10-5
Step 4: x 10-5

17. Multiplying in Scientific Notation Practice1.
1.) x 1010 2.
2.) x 103 3.
3.) x 10-6 4.
4.)

18. Dividing in Scientific Notation Part IV

19. Dividing in Scientific Notation Example # 4
𝟒.𝟐 𝒙 𝟏𝟎 𝟑 𝟐.𝟏 𝒙 𝟏𝟎 𝟏
Steps
Simplify:
Step 1 – Divide the terminating decimals. (4.2 ÷ 2.1)
Step 1: 4.2 ÷ 2.1 = 2
Step 2 – Subtract the exponents of 103 and 101
Step 2: 103 ÷ 101 =102
Step 3 – Rewrite step 1 and step 2 in scientific notation form.
Note: Always check to see if the decimals following the S.N rule.
Step 3: 2 x 102

20. Dividing in Scientific Notation Example # 5
𝟔.𝟗 𝒙 𝟏𝟎 𝟒 𝟐.𝟖𝟒 𝒙 𝟏𝟎 𝟓
Steps
Simplify:
Step 1 – Divide the terminating decimals. (6.9 ÷ 2.84)
Step 1: 6.9 ÷ 2.84 = 2.43
Step 2 – Subtract the exponents of 104 and 105 ( 4 – 5 = -1)
Step 2: 104 ÷ 105 =10-1
Step 3 – Rewrite step 1 and step 2 in scientific notation form.
Note: Always check to see if the decimals following the S.N rule.
Step 3: x 10-1

21. Dividing in Scientific Notation Example # 6
𝟓.𝟏 𝒙 𝟏𝟎 −𝟔 𝟔.𝟐 𝒙 𝟏𝟎 𝟓
Steps
Simplify:
Step 1 – Divide the terminating decimals. (5.1 ÷ 6.2)
Step 1: 5.𝟏÷ 6.2 = 0.822
Step 2 – Subtract the exponents of 10-6 and (-6 - 5= -11)
Step 2: ÷ 105 =10-11
Step 3 – Rewrite step 1 and step 2 in scientific notation form.
Step 3: x 10-11
Is this answer in S.N. form? Explain
Step 4: Change to 8.22 by moving decimal point one place to the right, and add -1 exponent to to make it 10-12
Step 4: x 10-12

22. Dividing in Scientific Notation Example # 7
𝟗 𝒙 𝟏𝟎 −𝟒 𝟐.𝟗 𝒙 𝟏𝟎 −𝟔
Steps
Simplify:
Step 1 – Divide the terminating decimals. (9 ÷ 2.9)
Step 1: 9 ÷ 2.9 = 3.103
Step 2 – Subtract the exponents of 10-4 and [-4 – (-6) = = 2]
Step 2: ÷ 10-6 =102
Step 3: x 102
Step 3 – Rewrite step 1 and step 2 in scientific notation form. Check to see if it is in the correct form.

23. Dividing in Scientific Notation Practice1. 2. 3. 4.

24. Summary
What are some important strategies you should remember when adding, subtracting, multiplying or dividing numbers in scientific notation?
What are some important things to remember when typing/reading scientific notation 0n a graphing calculator?
Do you have clear understanding on how to multiply or divide in scientific notation? Explain
Are there any more questions you may have using operations in scientific notation?