Math 5Using Exponents to Write

Numbers

Instructor: Mrs. Tew Turner

In this lesson we will learn how to read and write large

and small numbers using exponents.

Math Warm-up

5 32 4

In your Math Notebook

Multiply acrossMultiply downMultiply your results across and down.Put these answers in the triangles

==

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What do you notice about your results?

Try to use mental math.

In this lesson we will answer the question:

How can you read and write large and small numbers using exponents?

Vocabulary

exponential equation – a number sentence (either × or ÷) that includes an exponent

Ex. 4 × 102 or 7 ÷ 103

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

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

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

10 this is the base

2

In the last unit you learned about patterns in the Base 10 number

system.

Let’s review that information, too.

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

× 10

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

÷ 10

You also learned about exponents.

Let’s review what you learned about exponents.

10 base: 10 exponent: 4

10 x 10 x 10 x 10 =10,000

Ten thousands

4

10 base: 10 exponent: 5

10 x 10 x 10 x 10 x 10 = 100,000

Hundred Thousands

5

How can you use your knowledge of base 10 patterns

and exponents to read and write large and small

numbers?

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.

Let’s take a closer look:

4 x 102 = 4 x 10 x 10 = 400.

OR

4 x 100 = 400

Write 5,000 as an exponential equation.

5 x 1000 = 5000

1000 = 103

So, 5 x 103 = 5,000

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

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

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?

In your Math NotebookThe 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.

Look at these examples:

2 ÷ 101 = 2 ÷ 10 = 2/10 = 0.2

2 ÷ 102 = 2 ÷ 100 = 2/100 = 0.02

2 ÷ 103 = 2 ÷ 1000 = 2/1000 = 0.002

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?

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.

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

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

Write 0.006 as an exponent:

0.006 = 6 ÷ 1000

1000 written as an exponent is 103.

So, 6 ÷ 103 = 0.006

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

Copy this chart in your Math NotebookM

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Tho

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Hun

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Tens

One

s

Tent

hs

Hun

dred

ths

Tho

usan

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× 1

06

× 1

05

× 1

04

× 1

03

× 1

02

× 1

01

× 1

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÷ 10

1

÷ 10

2

÷ 10

3

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

What about writing 65,000 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

65,000.

What about writing 65,000 as an exponential equation?

Count…. 4 321×104

Step 3: Drop the zeros from the number.

6.50006.5 × 104

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 hundredth, so the exponent would be ÷102.

What about writing 0.78 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

0.78

What about writing 0.78 as an exponential equation?

Count…1 2÷102

Step 3: Drop the zeros from the number.

0 7878 ÷ 102

What about writing 0.78 as an exponential equation?

Guided PracticeWrite an an exponential equation.

1. 54,000

2. 870,000

3. 0.124

4. 0.35

Guided PracticeANSWERS

1. 54,000 5.4 × 104

2. 870,000 87 × 104

3. 0.124 124 ÷ 103

4. 0.35 35 ÷ 102

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

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.

1.3 0 0 .

The answer is 1,300

Write 53 ÷ 102 in standard form.

53 ÷ 100 = 53/100

You would move the decimal point two places to the left.

.53.

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.

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.

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.

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.

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.

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.

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.

Guided PracticeWrite the number in standard form.

1. 68 ÷ 103

2. 4.5 × 104

Guided PracticeWrite the number in standard form.

1. 68 ÷ 103 .068

2. 4.5 × 104 45,000

Write the following numbers as an exponent:

In your Math NotebookIndependent Practice

1. 6,0002. 0.43. 2904. 0.815. 82,000

Write the following numbers in standard form:

In your Math NotebookIndependent Practice

6. 3 × 105 7. 9 x 102

8. 1.4 ÷ 103

9. 7.9 ÷ 102

10. 4.63 × 106

Write the following numbers as an exponent:

1. 6,000 6 × 103

2. 0.4 4 ÷ 101

3. 290 2.9 × 102 4. 0.81 8.1 ÷ 101

5. 82,000 8.2 × 104

In your Math NotebookIndependent Practice ANSWERS

Write the following numbers in standard form:

In your Math NotebookIndependent Practice ANSWERS

6. 3 × 105 300,0007. 9 x 102 9008. 1 ÷ 103 0.0019. 7.9 ÷ 102 0.07910. 4.63 × 106 4,630,000

Lesson ReviewWriting 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.

Lesson ReviewWriting 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

Lesson ReviewWriting 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.

Lesson ReviewWriting 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.

Quick CheckIn your Math Notebook

Write the following as exponential equations1. 0.7342. 33

Write the following in standard form3. 6.2 × 105

4. 88 ÷ 103

Quick Check - ANSWERSIn your Math Notebook

Write the following as exponential equations1. 0.734 734 ÷ 103

2. 33 3.3 × 101

Write the following in standard form3. 6.2 × 105 620,0004. 88 ÷ 103 0.088

Today you learned how to write numbers using exponents.

Good Work with this

lesson.