Math 5 Using Exponents to Write Numbers Instructor: Mrs. Tew Turner
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
illio
ns
Hun
dred
T
hous
ands
Ten
Tho
usan
ds
Tho
usan
ds
Hun
dred
s
Tens
One
s
Tent
hs
Hun
dred
ths
Tho
usan
dths
× 1
06
× 1
05
× 1
04
× 1
03
× 1
02
× 1
01
× 1
00
÷ 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.