Warm Up: 2-10-14 Simplify the following. Them find the value Example: 2 2 ∙ 2 3 = 2 5 =32 3 9 ∙ 3 −7 100 23 0 12 −3 12 −5 6 10 ∙ 5 −3 5 −3 ∙ 6 8

Multiplying by Powers of 10

Patterns with Positive Powers of 10 Power of 10 Standard Form How many 0’s after the 1? How many times we moved the decimal point? 1.0× 10 0 1 1.0× 10 1 1.0× 10 2 1.0× 10 3 1.0× 10 4

Patterns with Positive Powers of 10 Power of 10 Standard Form How many 0’s after the 1? How many times we moved the decimal point? 1.0× 10 0 1 1.0× 10 1 10 1.0× 10 2 100 2 1.0× 10 3 1000 3 1.0× 10 4 10000 4

Analyzing Positive Powers of 10 What is the connection between the exponent on the 10 and the number of 0’s after the 1? ___________________________________________________________ __________________________________________________ What is the connection between the exponent on the 10 and the number of times we moved the decimal point? ___________________________________________________________ ___________________________________________________ What direction did we move the decimal point? ___________________________________________________________ ___________________________________________________________

Analyzing Positive Powers of 10 What is the connection between the exponent on the 10 and the number of 0’s after the 1? The exponent tells how many zeros are after the 1 What is the connection between the exponent on the 10 and the number of times we moved the decimal point? The exponent tells us how many times to move the decimal point What direction did we move the decimal point? Right

Guided Practice Using the information you just found, write the following in standard form 6.7 × 10 1 2. 6.1 × 10 4 3. 1.6 × 10 3 4. 3.46 × 10 2 5. 2.91 × 10 5 6. 8.651 × 10 7

Guided Practice Using the information you just found, write the following in standard form 6.7 × 10 1 =67 2. 6.1 × 10 4 =61000 3. 1.6 × 10 3 =1600 4. 3.46 × 10 2 =346 5. 2.91 × 10 5 =291000 6. 8.651 × 10 7 =86520000

Patterns with Negative Powers of 10 Power of 10 Standard Form How many 0’s after the decimal point? How many times we moved the decimal point? 1.0× 10 −5 0.00001 4 5 to the left 1.0× 10 −4 1.0× 10 −3 1.0× 10 −2 1.0× 10 −1

Patterns with Negative Powers of 10 Power of 10 Standard Form How many 0’s after the decimal point? How many times we moved the decimal point? 1.0× 10 −5 0.00001 4 5 to the left 1.0× 10 −4 0.0001 3 1.0× 10 −3 0.001 2 1.0× 10 −2 0.01 1 1.0× 10 −1 0.1

Analyzing Patterns with Negative Powers of 10 What is the connection between the exponent on 10 and the number of 0’s after the decimal point? ________________________________________________________ ________________________________________________________ What is the connection between the exponent on 10 and the number of times we move the decimal point? ________________________________________________________ ________________________________________________________ What direction are we moving the decimal when there is a negative exponent on the 10

Analyzing Patterns with Negative Powers of 10 What is the connection between the exponent on 10 and the number of 0’s after the decimal point? The number of 0’s is one less than the exponent What is the connection between the exponent on 10 and the number of times we move the decimal point? The exponent tells us how many times to move the decimal point What direction are we moving the decimal when there is a negative exponent on the 10? Left

Practice Using the information from the previous slide, write the following in standard form   7. 3.35 × 10 −1 8. 7.3 × 10 −6 9. 1.49 × 10 −7 10. 4.0027 × 10 −4 11. 5.2277 × 10 −3 12. 8.50284 × 10 −2

Practice Using the information from the previous slide, write the following in standard form   7. 3.35 × 10 −1 =0.335 8. 7.3 × 10 −6 =0.0000073 9. 1.49 × 10 −7 =.000000149 10. 4.0027 × 10 −4 =0.00040027 11. 5.2277 × 10 −3 =.0052277 12. 8.50284 × 10 −2 =0.0850284

What did we just find? We just found the standard form for Scientific Notation Scientific Notation is a way to write Small and Large numbers in a form that makes it easy to calculate and compare numbers that are too large or small to work with. We write Scientific Notation as a number between 1 and 10 multiplied by a power of 10

Writing Numbers in Scientific Notation

Writing Really Big Numbers into Scientific Notation Standard Form Re-writing into a number between 1 and 10 Number of numbers after the decimal point. Number of Times we moved the decimal point Scientific Notation 1,234.0 1.234 3 3 to the left 1.234× 10 3 1,2345 123,456 1,234,567 12,345,678

Writing Really Big Numbers into Scientific Notation Standard Form Re-writing into a number between 1 and 10 Number of numbers after the decimal point. Number of Times we moved the decimal point Scientific Notation 1,234.0 1.234 3 3 to the left 1.234× 10 3 1,2345 1.2345 4 1.2345× 10 4 123,456 1.23456 5 1.23456× 10 5 1,234,567 1.234567 6 1.234567× 10 6 12,345,678 1.2345678 7 1.2345678× 10 7

Analyzing Writing Big Numbers in Scientific Notation What kind of exponent do we use when writing Big Numbers into Scientific Notation? ______________________________________________________________________________ How do we know what positive number to use for the exponent on the 10 when we write a Big Number in Scientific Notation? ______________________________________________________________________________ What direction do we move the decimal point when writing big numbers in Scientific Notation? ______________________________________________________________________________ Why is the exponent positive when we write big numbers in Scientific Notation? ______________________________________________________________________________ What is the connection between the exponent on the 10 and the number of numbers after the decimal point? ______________________________________________________________________________

Analyzing Writing Big Numbers in Scientific Notation What kind of exponent do we use when writing Big Numbers into Scientific Notation? We use a positive exponent How do we know what positive number to use for the exponent on the 10 when we write a Big Number in Scientific Notation? We count how many times we move the decimal point What direction do we move the decimal point when writing big numbers in Scientific Notation? Right Why is the exponent positive when we write big numbers in Scientific Notation? ______________________________________________________________________________ What is the connection between the exponent on the 10 and the number of numbers after the decimal point? The exponent tells us how many numbers should be after the decimal point

Writing in Scientific Notation Write the following numbers in Scientific Notation 13. 34 14. 273 15. 79,700 16. 6,590 17. 4,733,800 18. 2,204,000,000

Writing in Scientific Notation Write the following numbers in Scientific Notation 13. 34 =3.4× 10 1 14. 273 15. 79,700=7.97× 10 4 16. 6,590 17. 4,733,800=4.733800× 10 6 18. 2,204,000,000

Writing Really Small Numbers into Scientific Notation Standard Form Re-writing into a number between 1 and 10 Number of Times we moved the decimal point Scientific Notation 0.12 01.2=1.2 1 to the right 1.2× 10 −1 0.022 0.0032 0.00042 0.000052

Analyzing Writing Really Small Numbers in Scientific Notation What kind of exponent for the 10 do we use when writing Small Numbers in Scientific Notation? _____________________________________________________ How do we know what the negative number will be for the exponent on the 10 when writing Small Numbers in Scientific Notation? _______________________________________________________ What direction do we move the decimal point when we write small numbers into Scientific Notation? ______________________________________________________ Why is the exponent negative when we write small numbers in Scientific Notation? __________________________________________________________

Analyzing Writing Really Small Numbers in Scientific Notation What kind of exponent for the 10 do we use when writing Small Numbers in Scientific Notation? Negative How do we know what the negative number will be for the exponent on the 10 when writing Small Numbers in Scientific Notation? Count how many times we moved the decimal What direction do we move the decimal point when we write small numbers into Scientific Notation? Right Why is the exponent negative when we write small numbers in Scientific Notation? _______________________________________________________ ___

Practice Write the following numbers in Scientific Notation 19. 0.00916 =9.16× 10 −3 20. 0.29 21. 0.00000571=5.71× 10 −5 22. 0.0008331 23. 0.0121=1.21× 10 −2 24. 0.00000018