Math 5 Using 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 = = = = 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?

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

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.

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 base: 10 exponent: 5 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. 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 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.

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 Notebook Thousands Hundred Thousands Ten Millions Thousands Hundreds Tens Ones Tenths Hundredths Thousandths × 105 × 104 × 106 × 103 × 102 × 101 × 100 ÷ 101 ÷ 102 ÷ 103

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

× 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…. 4 321

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

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.

× 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

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

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

Guided Practice ANSWERS 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.

Write the number in standard form. Guided Practice Write the number in standard form. 68 ÷ 103 2. 4.5 × 104

Write the number in standard form. Guided Practice Write the number in standard form. 68 ÷ 103 .068 2. 4.5 × 104 45,000

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

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 8. 1.4 ÷ 103 9. 7.9 ÷ 102 10. 4.63 × 106

Write the following numbers as an exponent: In your Math Notebook Independent Practice ANSWERS Write the following numbers as an exponent: 6,000 6 × 103 0.4 4 ÷ 101 290 2.9 × 102 0.81 8.1 ÷ 101 82,000 8.2 × 104

Write the following numbers in standard form: In your Math Notebook Independent Practice ANSWERS Write the following numbers in standard form: 6. 3 × 105 300,000 7. 9 x 102 900 8. 1 ÷ 103 0.001 9. 7.9 ÷ 102 0.079 10. 4.63 × 106 4,630,000

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.

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

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.

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.

Quick Check In your Math Notebook Write the following as exponential equations 1. 0.734 2. 33 Write the following in standard form 3. 6.2 × 105 4. 88 ÷ 103

Quick Check - ANSWERS In your Math Notebook Write the following as exponential equations 1. 0.734 734 ÷ 103 2. 33 3.3 × 101 Write the following in standard form 3. 6.2 × 105 620,000 4. 88 ÷ 103 0.088

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