Scientific Notation

Scientific Notation Why do we use scientific notation? Because in science we often deal with numbers which are ridiculously large or unimaginable small. For example:

Scientific Notation How many stars are in an average spiral galaxy? Answer: At least 200 Billion stars. or 200,000,000,000,000 stars.

Scientific Notation What is the distance between the electron and the nucleus of an atom? Answer: .0000000001 meters.

Scientific Notation It is not practical for us to work with numbers written as: 200,000,000,000 or .0000000001 So, we have come up with a way of dealing with these large and small numbers. And its called… Scientific Notation.

Correct Scientific Notation M x 10n Exponent (Order of Magnitude) + Positive for numbers greater than 1 - Negative for numbers less than 1 Mantissa A number from one to less than ten. Ex: 1.3, 3.4, 5.26

Scientific Notation Converting Large numbers to Scientific Notation. Example: 1,500,000 m Mantissa = 1.5 Exponent = 6, for 6 decimal places, and positive 1.5 x 106 m

Scientific Notation Converting Small numbers to Scientific Notation. Example: 0.000025 A Mantissa = 2.5 Exponent = -5, 5 for 5 decimal places, and negative 2.5 10-5 A

Scientific Notation The following two numbers are equal, however only one is expressed correctly. Which one? 17.5 x 105 m = 1.75 x 106 Answer: 1.75 x 106 m, the mantissa is a number from 1 - 10

Scientific Notation Special Case No. 1: 1 1 x 100 = _______ Remember, the exponent tells us how much to move the decimal. In this case the exponent is zero. So, the decimal remains where it is.

Scientific Notation Special Case No. 2: 10 1 x 101 = _______ 101 is like writing a word in shorthand or an abbreviation. It is implied that there is a “1 x” before the 101.

Scientific Notation Convert the following to scientific notation. 5.0 x 10-3 2.5 x 10-1 0.005 = ______________ 0.25 = _______________ 5.050 x 103 2.5 x 10-2 5,050 = ______________ 0.025 = ______________ 8 x 10-4 2.5 x 10-3 0.0008 = _____________ 0.0025 = _____________ 1 x 103 500 = _______________ 5 x 102 1,000 = ______________ 1 x 106 5,000 = ______________ 5 x 103 1,000,000 = __________

Scientific Notation Convert the following to standard notation. 1,500 .335 1.5 x 103 = __________________ 3.35 x 10-1 = __________________ .0015 .00012 1.5 x 10-3 = ____________ 1.2 x 10-4 = _____________ .0375 10,000 3.75 x 10-2 = _________________ 1 x 104 = _______________________ .1 375 1 x 10-1 = ________________________ 3.75 x 102 = ___________________ 220,000 4 x 100 = _______________ 4 2.2 x 105 = ____________________

Homework Answers Part B 1) 1,000,000 2) .00001 3) 100,000,000,000 Part A 1) 104 2) 10-3 3) 108 4) 3 x 107 5) 4.35 x 1011 6) 1.09 x 108 7) 6.78 x 107 8) 9 x 103 9) 6.02 x 10-1 10) 2.3 x 10-5 11) 5.43 x 101 12) 5.60 x 10-10 Part B 1) 1,000,000 2) .00001 3) 100,000,000,000 4) .0004 5) .0000067 6) 823,000,000 7) .00000001476 8) 7,680 9) .00004356 10) 2.85 11) 9,680,000,000,000 12) .000967