Scientific Notation Init 8/24/2011 by Daniel R. Barnes WARNING: This presentation includes images and other content taken from the world wide web without permission of the owners of that content. Do not copy or distribute this presentation. Its very existence may be illegal.
MATH PROBLEM: If the Chicxulub Sisters Copper Mine produces 670,000,000,000,000 tons of copper ore per year and a Xibalba-class cargo ship can haul 30,800,000 tons of copper ore, how many shiploads of copper ore does the mine produce each year? Seriously, you want us to divide 30,800,000 into 670,000,000,000,000? LONG DIVISION? 30,800,000 ) 670,000,000,000,000 ayfkm?
SWBAT . . . . . . convert numbers between regular format and scientific notation.
First, we must make sure we’ve learned about powers of ten.
SIMPLE POWERS of TEN 102 = 10 x 10 = 100 103 = 10 x 10 x 10 = 1000 105 = 10 x 10 x 10 x 10 x 10 = 100,000 101 = 10 = 10
SIMPLE POWERS of TEN 102 = 10 x 10 = 100 103 = 10 x 10 x 10 = 1000 105 = 10 x 10 x 10 x 10 x 10 = 100,000 101 = 10 = 10
NEGATIVE POWERS of TEN 1 1 10-1 = = = 0.1 101 10 1 1 1 10-2 = = = = 0.01 102 10 x 10 100 1 1 1 10-3 = = = = 0.001 103 10 x 10 x10 1000 10-4 1 1 1 = = = = 0.0001 104 10 x 10 x 10 x 10 10,000
NEGATIVE POWERS of TEN 1 1 10-1 = = = 0.1 101 10 1 1 1 10-2 = = = = 0.01 102 10 x 10 100 1 1 1 10-3 = = = = 0.001 103 10 x 10 x10 1000 10-4 1 1 1 = = = = 0.0001 104 10 x 10 x 10 x 10 10,000
TEN to the ZERO 103 = 1,000 102 = 100 101 = 10 100 = 1 10-1 = 0.1 10-2 = 0.01 10-3 = 0.001 Multiplying zero tens by each other sounds like one hand clapping, but seeing 100 placed in this sequence makes it obvious that it’s the only possible missing piece in the pattern.
TEN to the ZERO 103 = 1,000 102 = 100 101 = 10 100 = 1 10-1 = 0.1 10-2 = 0.01 10-3 = 0.001 Multiplying zero tens by each other sounds like one hand clapping, but seeing 100 placed in this sequence makes it obvious that it’s the only possible missing piece in the pattern.
Exponential form English word Decimal number Fractional form 1,000,000 106 one million 1,000,000 1 1,000 103 one thousand 1,000 1 One one-hundredth 1 1 10-2 0.01 = 100 102 One ten-thousandth 1 10-4 0.0001 10,000 1 100 one 1 1
Exponential form English word Decimal number Fractional form 1,000,000 106 one million 1,000,000 1 1,000 103 one thousand 1,000 1 One one-hundredth 1 1 10-2 0.01 = 100 102 One ten-thousandth 1 10-4 0.0001 10,000 1 100 one 1 1
Now Let’s throw in a multiplier. Okay. Now Let’s throw in a multiplier.
Exponential form English word Decimal number Fractional form 50 fifty 50 5 x 101 1 Twenty million 20,000,000 20,000,000 2 x 107 1 four one-thousandths 4 0.004 4 x 10-3 1000 Seven trillion 7 x 1012 7,000,000,000,000 Three One hundred millionths 3 3 x 10-8 0.00000003 100,000,000
Exponential form English word Decimal number Fractional form 50 fifty 50 5 x 101 1 Twenty million 20,000,000 20,000,000 2 x 107 1 four one-thousandths 4 0.004 4 x 10-3 1000 Seven trillion 7 x 1012 7,000,000,000,000 Three One hundred millionths 3 3 x 10-8 0.00000003 100,000,000
Now we can try converting a number to scientific notation. Alright. Now we can try converting a number to scientific notation.
2015 . Convert “2015” to scientific notation There’s a decimal point hiding in this number. Where is it? To where do we move the decimal point? 2015 . The first step in converting a number to scientific notation is to move the decimal until there’s one digit in front of it and however many digits are left behind it.
. 2.015 2015 Convert “2015” to scientific notation To where to we move the decimal point? . 2.015 2015 In this case, three spaces to the left.
2.015 x 103 Convert “2015” to scientific notation It looks like we just turned two thousand into two. That’s not right. That’s not what we’re trying to do. 2.015 x 103 To bring it back up to being about two thousand again, we need to multiply it by the right power of ten . . .
Convert “2015” to scientific notation 2015 = 2.015 x 103
Let’s practice with some more numbers.
Practice Question #1 465 = 4.65 x 102
Practice Question #2 30.7 = 3.07 x 101
Practice Question #3 400,000 = 4 x 105
Practice Question #4 13.1712 = 1.31712 x 101
Practice Question #5 0.32 = 3.2 x 10-1
Practice Question #6 0.00767 = 7.67 x 10-3
Practice Question #7 0.00000061 = 6.1 x 10-7
Practice Question #8 80,000,000,000 = 8 x 1010
Practice Question #9 0.000000091123 = 9.1123 x 10-8
Practice Question #10 0.009630041 = 9.630041 x 10-3
Practice Question #11 229,100,000 = 2.291 x 108
Practice Question #12 0.0000007212 = 7.212 x 10-7
Practice Question #13 39,700,000 = 3.97 x 107
That’s great, but, sometimes, you have a number that’s almost Okay. That’s great, but, sometimes, you have a number that’s almost in scientific notation, but not quite. What do you do? WHAT DO YOU DO?
Practice Question #14 56.2 x 1027 = 5.62 x 1028
Practice Question #15 0.09304 x 1013 = 9.304 x 1011
Practice Question #16 406.7 x 10-7 = 4.067 x 10-5
Practice Question #16 0.00393 x 10-24 = 3.93 x 10-27