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
21 22 23
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