Scientific Notation

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??

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. • 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 • 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. • 783 920 • 1 039 • 0.167 • 90.382 7 • 12.34

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

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. • 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 • 190 • 0.001 278 0 • 0.123 • 1.00 • 23 289 472 909

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. • 149 300 • 0.000 290 8 • 390.284 • 0.133 3 • 600 000 09 • 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. • 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. • 23 450 • 4.563 43 • 0.007 904 • 0.000 003 509 3 • 0.023 09 • 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. • 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. • 5 900 • 0.000 123 49 • 66.6 • 4.543 • 99 989 • 5.9 x 10^3 • 1.2349 x 10-4 • 6.66 x 10^1 • 4.543 x 100 • 9.9989 x 10^4

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

Scientific Notation