Essential Skills:Express numbers in scientific notation

Find products & quotients of numbers in scientific notation

Converting Standard Form → Scientific Notation◦ Step 1: Move the decimal point (left or right) until it is

to the right of the first non-zero digit◦ Step 2: Note the number of places you moved and

direction from step one◦ Step 3:

If the direction was to the left, the exponent is positive If the direction was to the right, the exponent is negative Write your answer as “a x 10n”, where n is your exponent

◦ Step 4: Remove the unnecessary zeros

Example 1A: Standard → Scientific◦ Express 4,062,000,000,000 in scientific notation

4,062,000,000,000

Moved 12 spaces to the left 4,062,000,000,000 = 4.062000000000 x 1012

4.062 x 1012

Example 1B: Standard → Scientific◦ Express 0.000000823 in scientific notation

0.000000823

Moved 7 spaces to the right 0.000000823 = 8.23 x 10-7

8.23 x 10-7

1 2 3 4

10%

0%

75%

15%

1. 4.58 x 106

2. 4.58 x 107

3. 4.58 x 108

4. 4.58 x 10-8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

1 2 3 4

0%

100%

0%0%

1. 4.52 x 104

2. 4.52 x 10-4

3. 4.52 x 105

4. 4.52 x 10-5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

Converting Scientific Notation → Standard Form◦ Step 1: Note whether the exponent n is positive or

negative◦ Step 2

If positive, move the decimal place to the right n spaces

If negative, move the decimal place to the left n spaces◦ Step 3: Insert the decimal point, zeros and commas

as needed

Example 2A: Scientific → Standard◦ Express 6.45 x 105 in standard form

Exponent means we move 5 spaces to the right 6.45

6.45 x 105 = 645000 645,000

000

Example 2B: Scientific → Standard◦ Express 1.8 x 10-3 in standard form

Exponent means we move 3 spaces to the left 1.8

1.8 x 10-3 = 0.0018 0.0018

000

1. 2. 3. 4

74%

5%0%

21%

1. 0.03162. 0.003163. 3.16004. 316

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

1. 2. 3 4

25% 25%25%25%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

1. 0.007612. 0.0007613. 7614. 7,610

4 Madison Roney

4 Jemikah Harrell

4 Isiah Hanlan

4 Jasmine Colon

4 Robert Porter

Assignment◦ Page 417 - 418◦ 1 – 9 & 21 – 35◦ Odd problems only

Day 2

Multiplying/Dividing numbers in scientific notation◦ Step 1: Multiply/Divide the non-exponent parts

together◦ Step 2: Multiply/Divide the exponent parts

together (meaning add/subtract the exponents)◦ Step 3: Readjust the non-exponent parts

If the value is > 10, shift the decimal point one space to the left and add one to the 10x exponent

If the value is < 1, shift the decimal point one space to the right and subtract one from the 10x exponent

Example 3: Evaluate (5 x 10-6)(2.3 x 1012)◦ (5)(2.3) = 11.5◦ (10-6)(1012) = 106

◦ 11.5 x 106

◦ 1.15 x 107

Example 4: Evaluate ◦ 4.5 ÷ 1.5 = 3◦ 108 ÷ 1010 = 10-2

◦ 3 x 10-2

8

10

4.5 x 10

1.5 x 10

1. 2 3 4

5%

68%

11%16%

1. 16.82. 1.68 x 101

3. 1.68 x 102

4. 1.68 x 103

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

1 2 3 4

0% 0%5%

95%

4

7

6.4 x 10

1.6 x 10

1. 4 x 103

2. 4 x 10-3

3. 4 x 10-2

4. 4 x 10-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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Last year Afyu’s state registered over 400 thousand watercraft. Boat sales in her state generated more than $15.4 million in state sales taxes the same year.

Example 5A: Express the number of watercraft registered and sales tax generated from boat sales last year in standard notation.◦ 400 thousand = 400,000◦ 15.4 million = 15,400,000

Last year Afyu’s state registered over 400 thousand watercraft. Boat sales in her state generated more than $15.4 million in state sales taxes the same year.

Example 5B: Write each number in scientific notation◦ 400,000 = 4 x 105

◦ 15,400,000 = 1.54 x 107

Last year Afyu’s state registered over 400 thousand watercraft. Boat sales in her state generated more than $15.4 million in state sales taxes the same year.

Example 5C: How many watercraft have been registered if 12 times the number last year have been registered in all?◦ (12)(4 x 105) = 48 x 105

◦ = 4.8 x 106

1 2 3 4

5%

95%

0%0%

1. 1500$120,000

2. 15,000$120,000

3. 150,000$1,002,000

4. 150,000$1,200,000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

1 2 3 4

5%

37%

53%

5%

1. 1.5 x 103

1.2 x 105

2. 1.5 x 104

1.2 x 105

3. 1.5 x 105

1.2 x 106

4. 1.5 x 105

1.2 x 107

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

1 2 3 4

50%

6%

11%

33%

1. 6 x 105

2. 6 x 104

3. 6 x 103

4. 6 x 102

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

9 Jemikah Harrell

9 Kaitlyn Phillips

8 Madison Roney

8 Jasmine Colon

8 Andrew Duncan

Assignment◦ Page 418◦ 37 – 49, odds