Powers of Ten

Learning Target: I can explain the relationship between a digit and how it is both ten times the number on its right and ten times less than the number on the left. Powers of Ten Day 1

Tenths, hundredths, and thousandths You may know that Place Value One tenth One hundredth One thousandth  

Tenths, hundredths, and thousandths You should also know Place Value Power of Ten One tenth 1 ÷ 10 One hundredth 1 ÷ 100 or 1 ÷ 10 x 10 One thousandth 1 ÷ 1000 or 1 ÷ 10 x 10 x 10

Powers of Ten As numbers get larger than 1, they are being multiplied by 10. As numbers get smaller than 1, they are being divided by 10. When you multiply 3 x 10, the answer is 30. You could also figure this out by moving the decimal to the right, shifting the numbers to the left. 3 can also be seen as 3.0 3.0 x 10 = 30.0

55 = 5 is ten times larger than 5 Powers of Ten When looking at a specific digit, it will always be ten times larger than the number to its left 55 = 5 is ten times larger than 5

Powers of Ten  

5 5 5 5 5 5 So that means 500 + 50 + 5 + + +

Turn and Talk A B C In the number 555.555 In 555.555 how much larger is the light blue 5 than the red 5? B C In 555.555 how much smaller is the light blue 5 than the red 5? In the number 555.555 Each 5 on the left is 10 times larger than the one on the right Each 5 on the right is 10 times smaller than the one on the left.

Turn and Talk A B C In the number 555.555 In 555.555 how much larger is the light blue 5 than the red 5? Ten times larger B In 555.555 how much larger is the light blue 5 than the red 5? One hundred times larger C In 555.555 how much smaller is the red 5 than the light blue 5 ? Ten times smaller In the number 555.555 Each 5 on the left is 10 times larger than the one on the right Each 5 on the right is 10 times smaller than the one on the left.

How is the value of the digit “2” in the number 15 How is the value of the digit “2” in the number 15.42 different from the value of the digit “2” in the number 12.54? 15.42 12.54

How is the value of the digit “2” in the number 15 How is the value of the digit “2” in the number 15.42 different from the value of the digit “2” in the number 12.54? 15.42 12.54 You could look at it as money, $0.02 You could look at it as money, $2.00

How is the value of the digit “2” in the number 15 How is the value of the digit “2” in the number 15.42 different from the value of the digit “2” in the number 12.54? 15.42 12.54 You could look at it as money, $0.02 You could look at it as money, $2.00

How is the value of the digit “2” in the number 15 How is the value of the digit “2” in the number 15.42 different from the value of the digit “2” in the number 12.54? 15.42 12.54 You could look at it as money, $0.02 The 2 in 15.42 is 100 times smaller than the the 2 in 12.54 You could look at it as money, $2.00 The 2 in 12.54 is 100 times larger than 0.02

Turn and Talk How is the value of the digit 1 in 1,000 different from the digit 1 in 0.001? 1,000 0.001 1000.000 .001

Turn and Talk  

Additional Examples What is the difference between the 3 in 0.034 and 3.4?

Try these on your own   3 . x 10 X 10

What is the difference between the 3 in 0.034 and 3.4? The 3 in 3.4 is in the ones place. The 3 in 0.034 is in the hundredths place. 3.0 .03

Review of Exponents and Scientific Notation What is the difference between the 3 in 0.034 and 3.4? The 3 in 3.4 is in the ones place. The 3 in 0.034 is in the hundredths place. 3.0 .03 If you divide 3.0 by 100, you will get 0.03.

Try in on your own then check with a shoulder buddy Look at the numbers 51.4 and 14.5. Explain what would happen to the value of the digit 5 if you moved it from the tens place to the tenths place? 51.4 14.5

Try in on your own then check with a shoulder buddy  

Dividing by Powers of Ten Look at the numbers 14.5 and 51.4 Look at the numbers 51.4 and 14.5. Explain what would happen to the value of the digit 4 if you moved it from the tenths place to the ones place? 51.4 14.5 The 4 in the ones place is ten times larger than the 4 in the tenths place (0.4). The value of the 4 would become ten times larger.

Review of Exponents and Scientific Notation What is the difference between the 6 in 6,100.45 and 6.92?

Review of Exponents and Scientific Notation  

Try on your own, check with a shoulder buddy Look at the numbers 13.546 and 365.49 Explain what happens to the value of 3 as you move it from the tens place to the hundreds place . Explain what happens to the value of the digit 6 as you move it from the thousandths place to the tens place.

Try on your own, check with a shoulder buddy  

Did you achieve your Learning Target Did you achieve your Learning Target? I can explain the relationship between a digit and how it is both ten times the number on its right and ten times less than the number on the left.

Powers of Ten Day 2

I can multiply a digit by powers of ten. Learning Target: I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left. I can multiply a digit by powers of ten.

Introduction to Powers of Ten forms "Powers of 10" is a very useful way of writing down large or small numbers. Instead of having lots of zeros, you show how many powers of 10 will make that many zeros Example: 5,000 = 5 × 1,000 = 5 × 103 Scientists and Engineers (who often use very big or very small numbers) like to write numbers this way. Example: The Mass of the Sun The Sun has a Mass of 1.988 × 1030 kg. It would be too hard to write 1,988,000,000,000,000,000,000,000,000,000 kg Cosmic Voyage Video Start at 6:43 and end at 11:40

Expanded Form and Powers of Ten The number 10,957,107 in expanded form shows the relationship between powers of ten and the way we can think about numbers in another way. 10,957,107 = 1 x 10,000,000 9 x 100,000 5 x 10,000 7 x 1,000 1 x 100 _+__________7 x 1 10,957,107

Multiplying by 10’s Place Value is based on powers of 10: Place Value Number of 10’s Multiplied 1 Billion 1,000,000,000 10x10x10x10x10x10x10x10x10 100 Million 100,000,000 10x10x10x10x10x10x10x10 10 Million 10,000,000 10x10x10x10x10x10x10 1 Million 1,000,000 10x10x10x10x10x10 100 Thousand 100,000 10x10x10x10x10 10 Thousand 10,000 10x10x10x10 1 Thousand 1,000 10x10x10 1 Hundred 100 10x10 1 Ten 10 1

Lets use exponents to show how numbers shift when multiplied by tens. 4 x 103 = 4 x 10 x 10 x 10 = 64 x 102 = 64 x 10 x 10 = 8.3 x 103 = 8.3 x 10 x 10 x 10 = 0.4 x 104 = 0.4 x 10 x 10 x10 x 10 = 102 = 10 x 10 105 = 10 x 10 x 10 x 10 x 10

You can use exponents to show how numbers shift. 4 x 103 = 4 x 10 x 10 x 10 = 4,000 64 x 102 = 64 x 10 x 10 = 6,400 8.3 x 103 = 8.3 x 10 x 10 x 10 = 8,300 0.4 x 104 = 0.4 x 10 x 10 x10 x 10 = 4,000 102 = 10 x 10 105 = 10 x 10 x 10 x 10 x 10

Try it on your own then check with a peer: EXPONENTS Try it on your own then check with a peer: 3 x 102 = 3 x 10 x 10 = 72 x 103 = 72 x 10 x 10 x 10 = 1.4 x 103 = 1.4 x 10 x 10 x 10 = 0.5 x 104 = 0.5 x 10 x 10 x10 x 10 = 102 = 10 x 10 105 = 10 x 10 x 10 x 10 x 10

Try it on your own then check with a peer: EXPONENTS Try it on your own then check with a peer: 3 x 102 = 3 x 100 = 300 72 x 103 = 72 x 1000 =72,000 1.4 x 103 = 1.4 x 1000 = 1,400 0.5 x 104 = 0.5 x 10,000 = 5,000 102 = 10 x 10 105 = 10 x 10 x 10 x 10 x 10

Try it on your own then check with a peer: EXPONENTS Try it on your own then check with a peer: 72 x 103 = 72 x 10 x 10 x 10 = You may see it this way, but… 1.4 x 103 = 1.4 x 10 x 10 x 10 = This is the proper way to write a decimal with powers of ten. 102 = 10 x 10 105 = 10 x 10 x 10 x 10 x 10

DECIMALS AND EXPONENTS Scientific Notation 10,000 = 10 x 10 x 10 x 10 = 100,000,000 =10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 500,000 =5 x 10 x 10 x 10 x 10 x 10= 1,500 = 1.5 x 10 x 10 x 10 = 1.5 x 103 When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out. 304,000 = 3.04 x 105 1,300,000 = 1.3 x 106 23,502,000 = 2.3502 x 107

DECIMALS AND EXPONENTS Scientific Notation 10,000 = 10 x 10 x 10 x 10 = 104 100,000,000 =10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 108 500,000 =5 x 10 x 10 x 10 x 10 x 10= 5 x 105 1,500 = 1.5 x 10 x 10 x 10 = 1.5 x 103 When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out. 304,000 = 3.04 x 105 1,300,000 = 1.3 x 106 23,502,000 = 2.3502 x 107

DECIMALS AND EXPONENTS Work on your own and check with a shoulder buddy: 100 = 10 x 10 = 1,000,000 =10 x 10 x 10 x 10 x 10 x 10 = 2,000,000= 2 x 10 x 10 x 10 x 10 x 10 x 10 = 320,000 = 3.2 x 10 x 10 x 10 x 10 x 10 = When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out. 304,000 = 3.04 x 105 1,300,000 = 1.3 x 106 23,502,000 = 2.3502 x 107

DECIMALS AND EXPONENTS Work on your own and check with a shoulder buddy: 100 = 10 x 10 = 102 1,000,000 =10 x 10 x 10 x 10 x 10 x 10 = 106 2,000,000= 2 x 10 x 10 x 10 x 10 x 10 x 10 = 2 x 106 320,000 = 3.2 x 10 x 10 x 10 x 10 x 10 = 3.2 x 105 When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out. 304,000 = 3.04 x 105 1,300,000 = 1.3 x 106 23,502,000 = 2.3502 x 107

I can multiply a digit by powers of ten. Did you achieve your Learning Targets? I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left. I can multiply a digit by powers of ten.

EXIT TICKET 555.555 What is the difference in the 5 and the 5? What is the relationship with a digit, and the digit to its left and right? (Ex. 3.33) What is the value of any number once you multiply it by 103 ? What is the value of 2.5 x 103 ? Write the 100,000 as an exponent (also known as scientific notation).

Powers of Ten Day 3

EXIT TICKET  

I can multiply and divide a digit by powers of ten. Learning Target: I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left. I can multiply and divide a digit by powers of ten.

Review of multiplying by 10’s Remember that Place Value is based on powers of 10: Place Value Number of 10’s Multiplied 1 Billion 1,000,000,000 10x10x10x10x10x10x10x10x10 100 Million 100,000,000 10x10x10x10x10x10x10x10 10 Million 10,000,000 10x10x10x10x10x10x10 1 Million 1,000,000 10x10x10x10x10x10 100 Thousand 100,000 10x10x10x10x10 10 Thousand 10,000 10x10x10x10 1 Thousand 1,000 10x10x10 1 Hundred 100 10x10 1 Ten 10 1

Tenths, hundredths, and thousandths You should also know Place Value Power of Ten One tenth 1 ÷ 10 One hundredth 1 ÷ 100 or 1 ÷ 10 x 10 One thousandth 1 ÷ 1000 or 1 ÷ 10 x 10 x 10 When you multiply by powers of ten, the decimal moves right. Ex. 47 x 100 = 4700 or 47.0 x 100 = 4,700.0 5.4 x 103= 5.4 x 103 = 5,400 or 5,400.0

Tenths, hundredths, and thousandths You should also know Place Value Power of Ten One tenth 1 ÷ 10 One hundredth 1 ÷ 100 or 1 ÷ 10 x 10 One thousandth 1 ÷ 1000 or 1 ÷ 10 x 10 x 10 Multiplying by 0.1 and dividing by ten have the same results. Multiplying by 0.01 and dividing by 100 have the same result. Multiplying by 0.001 and dividing by _____ have the same result.

Tenths, hundredths, and thousandths You should also know Place Value Power of Ten One tenth 1 ÷ 10 One hundredth 1 ÷ 100 or 1 ÷ 10 x 10 One thousandth 1 ÷ 1000 or 1 ÷ 10 x 10 x 10 Multiplying by 0.1 and dividing by ten have the same results. Multiplying by 0.01 and dividing by 100 have the same result. Multiplying by 0.001 and dividing by 1,000 have the same result.

Dividing with Powers of Ten  

You can use exponents to show how numbers shift when dividing. 7 x 10-3 = 7 x 0.1 x 0.1 x 0.1 = 22 x 10-2 = 22 ÷ 10 ÷ 10 = 8.3 x 10-3 = 8.3 x 0.1 x 0.1 x 0.1 = 0.4 x 10-4 = 0.4 ÷10 ÷10 ÷10 ÷10 = 10-2 = 0.1 x 0.1= 0.01 10-2 = 1 ÷ 10 ÷ 10 = 0.01 10-5 = 0.1 x 0.1 x 0.1 x 0.1 x 0.1= 0.00001 10-5 = ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 =

EXPONENTS You can use exponents to show how numbers shift when dividing. 7 x 10-3 = 7 x 0.1 x 0.1 x 0.1 = 0.007 22 x 10-2 = 22 ÷ 10 ÷ 10 = 0.22 8.3 x 10-3 = 8.3 x 0.1 x 0.1 x 0.1 = 0.0083 0.4 x 10-4 = 0.4 ÷10 ÷10 ÷10 ÷10 = 0.0004 10-2 = 0.1 x 0.1= 0.01 10-2 = 1 ÷ 10 ÷ 10 = 0.01 10-5 = 0.1 x 0.1 x 0.1 x 0.1 x 0.1= 0.00001 10-5 = ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 =

Try it on your own, check with a Shoulder Buddy EXPONENTS Try it on your own, check with a Shoulder Buddy 4 x 10-3 = 4 x 0.1 x 0.1 x 0.1 = 64 x 10-2 = 64 ÷10 ÷10 = 6.1 x 10-3 = 6.1 x 0.1 x 0.1 x 0.1 = 0.3 x 10-4 = 0.3 ÷10 ÷10 ÷10 ÷10 = 10-2 = 0.1 x 0.1= 0.01 10-5 = 0.1 x 0.1 x 0.1 x 0.1 x 0.1= 0.00001

EXPONENTS Try it on your own, check with a Shoulder Buddy 4 x 10-3 = 4 x 0.1 x 0.1 x 0.1 = 0.004 64 x 10-2 = 64 ÷10 ÷10 =0.64 6.1 x 10-3 = 6.1 x 0.1 x 0.1 x 0.1 = 0.0061 0.3 x 10-4 = 0.3 x 0.3 ÷10 ÷10 ÷10 ÷10 = 0.0003 10-2 = 0.1 x 0.1= 0.01 10-5 = 0.1 x 0.1 x 0.1 x 0.1 x 0.1= 0.00001

DECIMALS AND EXPONENTS   When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out. 0.051 = 5.1 x 10-2 0.1300= 1.3 x 10-1 0.96501 = 9.6501 x 10-1 0.000015 = 1.5 x 10-5 0.00411 = 4.11 x 10-3

DECIMALS AND EXPONENTS   When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out. 0.051 = 5.1 x 10-2 0.1300= 1.3 x 10-1 0.96501 = 9.6501 x 10-1 0.000015 = 1.5 x 10-5 0.00411 = 4.11 x 10-3

DECIMALS AND EXPONENTS Scientific Notation 0.00002 = 2 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 0.00005 = 0.00444= 0.00000089 = When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out. 0.051 = 5.1 x 10-2 0.1300= 1.3 x 10-1 0.96501 = 9.6501 x 10-1 0.000015 = 1.5 x 10-5 0.00411 = 4.11 x 10-3

DECIMALS AND EXPONENTS Scientific Notation 0.00002 = 2 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 = 2 x 10-5 0.00005 = 5 x 10-5 0.00444= 4.44 x 10-3 0.00000089 = 8.9 x 10-7 When given a number that has more than one non-zero number, you tend to write the decimal after the first “non-zero” number. You must include the other non-zero numbers in the decimal number. Zeros that follow can be left out. 0.051 = 5.1 x 10-2 0.1300= 1.3 x 10-1 0.96501 = 9.6501 x 10-1 0.000015 = 1.5 x 10-5 0.00411 = 4.11 x 10-3

DECIMALS AND EXPONENTS Scientific Notation 0.00002 = 2 ÷10 ÷10 ÷10 ÷10 ÷10 = 2 ÷10-5 0.00005 = 5 ÷10-5 Try these one your own: 0.00444= 0.00000089 = At times you’ll see exponents this way: 4,500 ÷ 103 = 4.5 290,400,000 ÷ 105 = Dividing by powers or ten is the same as multiplying by negative powers of ten.

DECIMALS AND EXPONENTS Scientific Notation 0.00002 = 2 ÷10 ÷10 ÷10 ÷10 = 2 ÷104 0.00005 = 5 ÷105 0.00444= 4.44 ÷ 103 0.00000089 =8.9 ÷ 107 At times you’ll see exponents this way: 4,500 ÷ 103 = 4.5 290,400,000 ÷ 105 = Dividing by powers or ten is the same as multiplying by negative powers of ten.

I can multiply and divide a digit by powers of ten. Did you achieve your Learning Target? I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left. I can multiply and divide a digit by powers of ten.

EXIT TICKET 555.555 What is the difference in the 5 and the 5? What is the value of any number once you multiply it by 10-3 ? What is the value of 1.05 x 10-3 ? What is 3.04 ÷ 103 ? Write the 0.00001 as an exponent (also known as scientific notation).

Powers of Ten Day 4

I can multiply and divide a digit by powers of ten. Learning Target: I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left. I can multiply and divide a digit by powers of ten.

REVIEW YESTERDAYS EXIT TICKET  

Practice Powers of Ten What is 100.4 x 104 ? What is 5.567 x 102 ?

Powers of Ten What is 100.4 x 104 ? 1,004,000 What is 5.567 x 102 ? 556.7 What is 6.6 x 10-2 ? 0.066 What is 372 ÷ 105 ? 0.00372

8 thousandths Practice Powers of Ten Which value is ten times the value of the digit 7 in 509.171? 7 tens 7 ones 7 tenths 7 hundredths

Practice Powers of Ten The value of 7 in 509.171 = 0.07 8 thousandths Practice Powers of Ten Which value is ten times the value of the digit 7 in 509.171? 7 tens 7 ones 7 tenths 7 hundredths The value of 7 in 509.171 = 0.07 0.07 x 10 = 0.7, which is 7 tenths

Powers of Ten If 1,097 x 10n = 10,970, what is the value of n? n = stands for an “unknown” number. What could be the exponent that would make this equation true?

Powers of Ten If 1,097 x 10n = 10,970, what is the value of n? n = stands for an “unknown” number. What could be the exponent that would make this equation true? 1,097 is ten times smaller than 10,970. The opposite operation, of dividing by ten is multiplying by ten so 1,097 x 10n = 10,970, n = 1

Try on you own, then check with a shoulder buddy If 1,097 x 10n = 109,700,000 what is the value of n? If 3.3 x 10n = 3,300 what is the value of n? If 3.3 x 10n = 0.033, what is the value of n? If 64 ÷ 10n = 0.0064, what is the value of n?

Try on you own, then check with a shoulder buddy If 1,097 x 10n = 109,700,000 what is the value of n? n = 5 because 1,097 x 105 = 109,700,000 If 3.3 x 10n = 3,300 what is the value of n? n = 3 because 3.3 x 103 = 3,300 If 3.3 x 10n = 0.033, what is the value of n? n = -2 because 3.3 x 10-2 = 0.033 If 64 ÷ 10n = 0.0064, what is the value of n? n = 4 because 64 ÷ 104 = 0.0064

More Practice with Powers of Ten Annie had the answer 35.65 showing on her calculator after dividing a number by ten. What was the original number? Explain how you know.

Dividing with Powers of Ten  

Powers of Ten Explain what happens to the value of the digits when multiplied and divided by a power of 10 using the two examples below. 2,500 ÷ 103 2.5 x 103

Powers of Ten  

I can multiply and divide a digit by powers of ten. Did you achieve your Learning Target? I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left. I can multiply and divide a digit by powers of ten.

I can multiply and divide a digit by powers of ten. Any questions? Did you achieve your Learning Target? I can explain the relationship between a digit and how it is either ten times the number on its right and ten times less than the number on the left. I can multiply and divide a digit by powers of ten.

Great, now please clear off your desk You will need a sheet of notebook paper and a sharpened pencil for your 1st quick quiz common assessment in math!