1. Math 5 Using Exponents to Write Numbers
Instructor: Mrs. Tew Turner

2. In this lesson we will learn how to read and write large and small numbers using exponents.

3. Math Warm-up = = = = In your Math Notebook Multiply across
Multiply down
Multiply your results across and down.
Put these answers in the triangles
Try to use mental math. 5 3 2 4 = = = =
What do you notice about your results?

4. In this lesson we will answer the question:
How can you read and write large and small numbers using exponents?

5. Vocabulary
exponential equation – a number sentence (either × or ÷) that includes an exponent
Ex. 4 × 102 or 7 ÷ 103

6. Vocabulary
exponent - the exponent of a number shows you how many times the number is to be used in a multiplication.
It is written as a small number to the right and above the base number.
example: 102 = 10 × 10 = 100

7. An exponent is written to the right of a number and looks like it is sitting on the shoulder of the number.
this is the exponent 10 2

8. The base is the number that you use as a factor in the multiplication of an exponential equation.10
this is the base 2

9. Let’s review that information, too.
In the last unit you learned about patterns in the Base 10 number system.
Let’s review that information, too.

10. As you move to the left in the base 10 system, the place is multiplied by 10. The values get larger.
× 10

11. As you move to the right in the base 10 system, the place is divided by 10. The values get smaller.
÷ 10

12. You also learned about exponents.
Let’s review what you learned about exponents.

13. 10 base: 10 exponent: 4 10 base: 10 exponent: 5 4
10 x 10 x 10 x 10 =10,000
Ten thousands 4
10 base: exponent: 5
10 x 10 x 10 x 10 x 10 = 100,000
Hundred Thousands 5

14. How can you use your knowledge of base 10 patterns and exponents to read and write large and small numbers?

15. Let’s look at this example:
I want to write 400 as an exponential equation.
How can I do that?
I know that 102 = 100.
So, 4 x 102 = 400.

16. Let’s take a closer look:
4 x 102 = 4 x 10 x 10 = 400. OR
4 x 100 = 400

17. Write 5,000 as an exponential equation.
1000 = 103
So, 5 x 103 = 5,000

18. Look at these examples:
3.6 × 101 = 3.6 × 10 = 36.
3.6 × 102 = 3.6 × 10 × 10 = 360
3.6 × 103 = 3.6 × 10 × 10 × 10 = 3,600

19. Look at these examples:
3.6 × 104 = 3.6 × 10 × 10 × 10 × 10 = 36,000
3.6 × 105 = 3.6 × 10 × 10 × 10 × 10 × 10 = 360,000
3.6 × 106 = 3.6 × 10 × 10 × 10 × 10 × 10 × 10 = 3,600,000

20. In your Math Notebook
What pattern do you notice about the relationship between the movement of the decimal point from the factor to the product and the multiplication by the powers of 10?

21. In your Math Notebook
The decimal point moves one space to the right for each power of 10 by which the factor is multiplied.
Ex. 3.6 × 102 = 3.6 × 10 × 10 = 360
The factor 3.6 is multiplied by ten to the second power, so the decimal point moved 2 spaces to the right.

22. Look at these examples:
2 ÷ 101 = 2 ÷ 10 = 2/10 = 0.2
2 ÷ 102 = 2 ÷ = 2/100 = 0.02
2 ÷ 103 = 2 ÷ = 2/1000 = 0.002

23. In your Math Notebook
What pattern do you notice about the relationship between the movement of the decimal point from the dividend to the quotient and the division by the powers of 10?

24. In your Math Notebook
The decimal point moves one space to the left for each power of 10 by which the dividend is divided.
Ex. 2 ÷ 102 = 2 ÷ 100 = 0.02
The dividend is divided by ten to the second power, so the decimal point moved 2 spaces to the left.

25. What if you want to write a decimal as an exponential equation?

26. Let’s look at this example:
I want to write 0.03 as an exponent.
How can I do that?
0.03 = 3 ÷ 100
100 written as an exponent is 102.
So, 3 ÷ 102 = 0.03

27. Write as an exponent:
0.006 = 6 ÷ 1000
1000 written as an exponent is 103.
So, 6 ÷ 103 = 0.006

28. When working with writing numbers as exponents, it would make it easier to make a chart that assigns exponents to place values.

29. Copy this chart in your Math Notebook
Thousands
Hundred
Thousands
Ten
Millions
Thousands
Hundreds
Tens
Ones
Tenths
Hundredths
Thousandths
× 105
× 104
× 106
× 103
× 102
× 101
× 100
÷ 101
÷ 102
÷ 103

30. What about writing 65,000 as an exponential equation?
Step 1: Figure out what the exponent would be, using the place value chart you copied in your Math Notebook
This is to the ten thousands place, so the exponent would be ×104

31. × move the decimal to the left ÷ move the decimal to the right 65,000.
Step 2: Move the decimal place the number of places of the exponent. The × or ÷ will tell you the direction.
× move the decimal to the left
÷ move the decimal to the right
65,000.
What about writing 65,000 as an exponential equation?
×104
Count…

32. Step 3: Drop the zeros from the number. 6.5000 6.5 × 104
What about writing 65,000 as an exponential equation?
Step 3: Drop the zeros from the number.
6.5000
6.5 × 104

33. What about writing 0.78 as an exponential equation?
Step 1: Figure out what the exponent would be using the place value chart you copied in your Math Notebook
This is to the hundredth, so the exponent would be ÷102.

34. × move the decimal to the left ÷ move the decimal to the right 0.78
Step 2: Move the decimal place the number of places of the exponent. The × or ÷ will tell you the direction.
× move the decimal to the left
÷ move the decimal to the right
0.78
What about writing 0.78 as an exponential equation?
÷102
Count…1 2

35. Step 3: Drop the zeros from the number. 0 78 78 ÷ 102
What about writing 0.78 as an exponential equation?
Step 3: Drop the zeros from the number.
0 78
78 ÷ 102

36. Write an an exponential equation.
Guided Practice
Write an an exponential equation.
54,000
2. 870,000
0.124
0.35

37. Guided Practice
ANSWERS
54, × 104
2. 870, × 104
÷ 103
÷ 102

38. Now, how do you write an exponent in standard form?

39. Write 1.3 × 103 in standard form.
1.3 × 10 × 10 × 10 = 1.3 × 1,000
So, you would move the decimal point three places to the right.
The answer is 1,300

40. Write 53 ÷ 102 in standard form.
53 ÷ 100 = 53/100
You would move the decimal point two places to the left.
.53.

41. Write 53 ÷ 102 in standard form.
53 ÷ 100 = 53/100 = 0.53
Sometimes it is easier to write a number as a decimal from an exponent when you write it as a fraction first.

42. Writing a number in standard form from an exponential equation:
Step 1: Look at the order of operation to see which direction you are moving the decimal point.
× move the decimal to the right
÷ move the decimal to the left
**Note: This is the opposite of writing a number as an exponent.

43. Writing a number in standard form from an exponential equation:
Step 1: Look at the order of operation to see which direction you are moving the decimal point.
× move the decimal to the right
÷ move the decimal to the left
Ex. 3.5 × 103
This is ×, so the decimal will move to the right.

44. Writing a number in standard form from an exponential equation:
Step 2: Look at the power of ten to see how many places you will move the decimal point.
Ex. 3.5 × 103
This is to the power of 3, so you would move the decimal three places.
3.500.

45. Writing a number in standard form from an exponential equation:
Step 1: Look at the order of operation to see which direction you are moving the decimal point.
× move the decimal to the right
÷ move the decimal to the left
**Note: This is the opposite of writing a number as an exponent.

46. Writing a number in standard form from an exponential equation:
Step 1: Look at the order of operation to see which direction you are moving the decimal point.
× move the decimal to the right
÷ move the decimal to the left
Ex. 5 ÷ 102
This is ÷, so the decimal will move to the left.

47. Writing a number in standard form from an exponential equation:
Step 2: Look at the power of ten to see how many places you will move the decimal point.
Ex. 5 ÷ 102
This is to the power of 2, so you would move the decimal two places.
0.05.

48. Write the number in standard form.
Guided Practice
Write the number in standard form.
68 ÷ 103
× 104

49. Write the number in standard form.
Guided Practice
Write the number in standard form.
68 ÷
× ,000

50. Write the following numbers as an exponent:
In your Math Notebook
Independent Practice
Write the following numbers as an exponent:
6,000
0.4
290
0.81
82,000

51. Write the following numbers in standard form:
In your Math Notebook
Independent Practice
Write the following numbers in standard form:
6. 3 × 105
7. 9 x 102
÷ 103
÷ 102
× 106

52. Write the following numbers as an exponent:
In your Math Notebook
Independent Practice ANSWERS
Write the following numbers as an exponent:
6, × 103
÷ 101
× 102
÷ 101
82, × 104

53. Write the following numbers in standard form:
In your Math Notebook
Independent Practice ANSWERS
Write the following numbers in standard form:
6. 3 × ,000
7. 9 x
8. 1 ÷ ÷
× ,630,000

54. Writing a whole number as an exponential equation
Lesson Review
Writing a whole number as an exponential equation
Step 1: Figure out what the exponent would be, using the place value chart you copied in your Math Notebook.

55. Writing a whole number as an exponential equation
Lesson Review
Writing a whole number as an exponential equation
Step 2: Move the decimal place the number of places of the exponent. The × or ÷ will tell you the direction.
× move the decimal to the left
÷ move the decimal to the right

56. Lesson Review
Writing a number in standard form from an exponential equation:
Step 1: Look at the order of operation to see which direction you are moving the decimal point.
× move the decimal to the right
÷ move the decimal to the left
**Note: This is the opposite of writing a number as an exponent.

57. Lesson Review
Writing a number in standard form from an exponential equation:
Step 2: Look at the power of ten to see how many places you will move the decimal point.

58. Quick Check In your Math Notebook
Write the following as exponential equations
2. 33
Write the following in standard form
× 105
÷ 103

59. Quick Check - ANSWERS In your Math Notebook
Write the following as exponential equations
÷ 103
× 101
Write the following in standard form
× ,000 ÷

60. Good Work with this lesson.
Today you learned how to write numbers using exponents.