1. Adding/Subtracting/Multiplying/Dividing Numbers in Scientific Notation

2. How wide is our universe?
210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

3. A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer

4. An easy way to remember this is:
If an exponent is positive, the number gets larger, so move the decimal to the right.
If an exponent is negative, the number gets smaller, so move the decimal to the left.

5. When changing from Standard Notation to Scientific Notation:
4) See if the original number is greater than or less than one.
If the number is greater than one, the exponent will be positive.
= x 105
If the number is less than one, the exponent will be negative.
= 6.72 x 10-8

6. Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make this number be between 1 and 10?
Between the 2 and the 1

7. 2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal? 23
When the original number is more than 1, the exponent is positive.
The answer in scientific notation is
2.1 x 1023

8. Write 28750.9 in scientific notation.
x 10-5
x 10-4
x 104
x 105

9. 2) Express 1.8 x 10-4 in decimal notation.
3) Express 4.58 x 106 in decimal notation.
4,580,000

10. Try changing these numbers from Scientific Notation to Standard Notation:
9.678 x 104
x 10-3
x 107
x 10-5
96780

11. Write in PROPER scientific notation
Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) x 109
2.346 x 1011
9) x 104
6.42 x 10 2

12. Adding/Subtracting when Exponents are Equal
When the exponents are the same for all the numbers you are working with, add/subtract the base numbers then simply put the given exponent on the 10.

13. General Formulas (N X 10x) + (M X 10x) = (N + M) X 10x
(N X 10y) - (M X 10y) = (N-M) X 10y

14. Example 1 Given: 2.56 X 103 + 6.964 X 103 Add: 2.56 + 6.964 = 9.524
Answer: X 103

15. Example 2
Given: 9.49 X 105 – X 105
Subtract: 9.49 – = 4.627
Answer: X 105

16. Adding With the Same Exponent
(3.45 x 103) + (6.11 x 103)
= 9.56
9.56 x 103

17. Subtracting With the Same Exponent
(8.96 x 107) – (3.41 x 107)
8.96 – 3.41 = 5.55
5.55 x 107

18. Adding/Subtracting when the Exponents are Different

19. When adding or subtracting numbers in scientific notation, the exponents must be the same.
If they are different, you must move the decimal either right or left so that they will have the same exponent.

20. Moving the Decimal
For each move of the decimal to the right you have to add -1 to the exponent.
For each move of the decimal to the left you have to add +1 to the exponent.

21. Continued…
It does not matter which number you decide to move the decimal on, but remember that in the end both numbers have to have the same exponent on the 10.

22. Example 1
Given: 2.46 X X 103
Shift decimal 3 places to the left for 103.
Move: X 103+3
Add: 2.46 X X 106
Answer: X 106

23. Example 2
Given: X 103 – 2.65 X 10-1
Shift decimal 4 places to the right for 10-1.
Move: X 10(-1+4)
Subtract: X X 103
Answer: X 103

24. (4.12 x 106) + (3.94 x 104)
(412 x 104) + (3.94 x 104) =
x 104
Express in proper form: 4.15 x 106

25. Subtracting With Different Exponents
(4.23 x 103) – (9.56 x 102)
(42.3 x 102) – (9.56 x 102)
42.3 – 9.56 = 32.74
32.74 x 102
Express in proper form: 3.27 x 103

26. Multiplying… The general format for multiplying is as follows…
(N x 10x)(M x 10y) = (N)(M) x 10x+y
First multiply the N and M numbers together and express an answer.
Secondly multiply the exponential parts together by adding the exponents together.

27. Multiplying…
Finally multiply the two results for the final answer.
(2.41 x 104)(3.09 x 102)
2.41 x 3.09 = 7.45
4 + 2 = 6
7.45 x 106

28. 7) evaluate (3,600,000,000)(23). The answer in scientific notation is
8.28 x 10 10
The answer in decimal notation is
82,800,000,000

29. 6) evaluate (0.0042)(330,000). The answer in decimal notation is 1386
The answer in scientific notation is
1.386 x 103

30. Write (2.8 x 103)(5.1 x 10-7) in scientific notation.

31. Now it’s your turn.
Use the link below to practice multiplying numbers in scientific notation.
Multiplying in Scientific Notation

32. Dividing… The general format for dividing is as follows…
(N x 10x)/(M x 10y) = (N/M) x 10x-y
First divide the N number by the M number and express as an answer.
Secondly divide the exponential parts by subtracting the exponent from the exponent in the upper number.

33. Dividing…
Finally divide the two results together to get the final answer.
(4.89 x 107)/(2.74 x 104)
4.89 / 2.74 = 1.78
7 – 4 = 3
1.78 x 103

34. 5) evaluate: x x 102 :
The answer in scientific notation is
6 x
The answer in decimal notation is

35. 0.0028125 Write in scientific notation. 2.8125 x 10-3
4) Evaluate: x x 10-2
Write in scientific notation.
x 10-3

36. Now it’s your turn.
Use the link below to practice dividing numbers in scientific notation.
Dividing in Scientific Notation

37. Practice Adding and Subtracting in Scientific Notation
Practice Worksheet
Practice Adding and Subtracting in Scientific Notation
Answers to Worksheet

38. Links for more information and practice
Addition and Subtraction with Scientific Notation
Problem Solving--Scientific Notation
Scientific Notation

39. Quiz Time!!!
Below is a set of links for a quiz on adding and subtracting numbers in scientific notation, and there is a link to get the answers to the quiz.
Adding and Subtracting Quiz
Answers to Quiz