Scientific Notation

What is Scientific Notation? Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise.

Why use scientific notation? For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. Numbers expressed in scientific notation can be used in a computation with far greater ease.

Scientific notation consists of two parts: A number that is 1 or greater but less than 10 Multiplied by a power of 10 N x 10x

Are the following in scientific notation?? 23.983 93 x 10^9 4.193 859 30 x 104 98 920.188 438 x 10^-3 2.222 21 x 10 000 9.002 x 100 3.999 293 4 x 10^1 0.110 382 749 392 092 028 475 7 x 102 1.00x 10^56 2.394 03 x 10-23 9.000 78 x 10^-1

Are the following in scientific notation?? 23.983 93 x 10^9 No 4.193 859 30 x 104 Yes 98 920.188 438 x 10^-3 2.222 21 x 10 000 9.002 x 100 3.999 293 4 x 10^1 0.110 382 749 392 092 028 475 7 x 102 1.00x 10^56 2.394 03 x 10-23 9.000 78 x 10^-1

Changing standard form to scientific notation.

To change standard form to scientific notation… Place the decimal point so that there is one non-zero digit to the left of the decimal point. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

Continued… If the original number was less than 1, then the exponent is negative. If the original number was 10 or greater, then the exponent is positive. If the original number was less than 10 (9.999) but 1 or greater (1 or 1.111 11), then the exponent is zero (0) which means the number is multiplied by 1. 6 x 100 = 6 (10 to the power of zero equals one)

Example 1 Given: 289 800 000 Use: 2.898 (moved 8 places) Answer: 2.898 x 108

Example 2 Given: 0.000 567 Use: 5.67 (moved 4 places) Answer: 5.67 x 10-4

Change each of the following standard form numbers into scientific notation. 378 000 0.009 34 0.000 000 983 1.928 4 34.903

Change each of the following standard form numbers into scientific notation. 378 000 0.009 34 0.000 000 983 1.928 4 34.903 3.78 x 105 9.34 x 10^-3 9.83 x 10-7 1.928 4 x 10^0 3.940 3 x 101

Change each of the following standard form numbers into scientific notation. 783 920 1 039 0.167 90.382 7 12.34

Change each of the following standard form numbers into scientific notation. 783 920 1 039 0.167 90.382 7 12.34 7.839 2 x 105 1.039 x 10^3 1.67 x 10-1 9.038 27 x 10^1 1.234 x 101

Change each of the following standard form numbers into scientific notation. 190 0.001 278 0 0.123 1.00 23 289 472 909

Change each of the following standard form numbers into scientific notation. 190 0.001 278 0 0.123 1.00 23 289 472 909 1.9 x 102 1.278 0 x 10^-3 1.23 x 10-1 1 x 100 2.328 947 290 9 x 10^10

Changing scientific notation to standard form.

To change scientific notation to standard form… Simply move the decimal point to the right for positive exponent 10. Move the decimal point to the left for negative exponent 10. For 10^0, just drop the 10^0. (Use zeros to fill in places.)

Example 3 Given: 5.093 x 106 Answer: 5 093 000 (moved 6 places to the right)

Example 4 Given: 1.976 x 10-4 Answer: 0.000 197 6 (moved 4 places to the left)

Change each of the following numbers in scientific notation into standard form numbers. 1.493 x 105 2.908 x 10^-4 3.902 84 x 102 1.333 x 10-1 6.000 000 9 x 10^7

Change each of the following numbers in scientific notation into standard form numbers. 1.493 x 105 2.908 x 10^-4 3.902 84 x 102 1.333 x 10-1 6.000 000 9 x 10^7 149 300 0.000 290 8 390.284 0.133 3 600 000 09

Change each of the following numbers in scientific notation into standard form numbers. 2.345 x 104 4.56343 x 100 7.904 x 10^-3 3.5093 x 10-6 2.309 x 10-2

Change each of the following numbers in scientific notation into standard form numbers. 2.345 x 104 4.56343 x 100 7.904 x 10^-3 3.5093 x 10-6 2.309 x 10-2 23 450 4.563 43 0.007 904 0.000 003 509 3 0.023 09

Change each of the following numbers in scientific notation into standard form numbers. 5.9 x 10^3 1.2349 x 10-4 6.66 x 10^1 4.543 x 100 9.9989 x 10^4

Change each of the following numbers in scientific notation into standard form numbers. 5.9 x 10^3 1.2349 x 10-4 6.66 x 10^1 4.543 x 100 9.9989 x 10^4 5 900 0.000 123 49 66.6 4.543 99 989

Even More Practice Below is a list of links to games and activities all having to do with scientific notation. http://www.aaamath.com/dec71i-dec2sci.html http://janus.astro.umd.edu/cgi-bin/astro/scinote.pl http://www.xpmath.com/forums/arcade.php?do=play&gameid=21#.Ubu80-vF1b0