© 2010 Pearson Prentice Hall. All rights reserved Scientific Notation § 9.5

Tobey & Slater, Basic College Mathematics, 6e2 Scientific Notation 5600 = 5.6  1000 = 5.6  10 3 greater than 1 and less than 10 a power of 10 78,200,000 = 7.82  = 7.82  10 7 Scientific notation A positive number is in scientific notation if it is in the form a  10n, where a is a number greater than (or equal to) 1 and less than 10, and n is an integer.

Tobey & Slater, Basic College Mathematics, 6e3 Standard Notation to Scientific Notation Example: Write 67,300 in scientific notation. 67,300. = 6.73  10 Starting position of decimal point Ending position of decimal point What power? The decimal point was moved 4 places to the left, so we use a power of 4. 67,300 = 6.73  10 4 A number that is larger than 10 and written in scientific notation will always have a positive exponent as the power of 10.

Tobey & Slater, Basic College Mathematics, 6e4 Negative Exponents 10 3 = = = =1 10 –1 = –2 = –3 =0.001 Notice the following pattern when raising a base of 10 to positive and negative exponents. The positive exponent indicates the number of places to move the decimal place to the right. The negative exponent indicates the number of places to move the decimal place to the left. Any number to the zero power is 1.

Tobey & Slater, Basic College Mathematics, 6e5 Standard Notation to Scientific Notation Example: Write in scientific notation = 4.8  10 Starting position of decimal point Ending position of decimal point What power? The decimal point was moved 2 places to the right, so we use a power of – = 4.8  10 –2 A number that is smaller than 1 and written in scientific notation will always have a negative exponent as the power of 10.

Tobey & Slater, Basic College Mathematics, 6e6 Scientific Notation to Standard Notation Example: Write 9.1  10 4 in standard notation. 9.1  10 4 =  10 4 = 91,000 Move the decimal point 4 places to the right. Example: Write 6.72  10 –3 in standard notation  10 –3 = 6.72  10 –3 = Move the decimal point 3 places to the left.

Tobey & Slater, Basic College Mathematics, 6e7 Adding and Subtracting in Scientific Notation Numbers in scientific notation may be added or subtracted if they have the same power of 10. We add or subtract the decimal part and leave the power of 10 unchanged. Example: Add      10 8 Add the decimal part. Leave the power of 10 unchanged. Example: Subtract  10 4 – 1.78   10 5 – 1.78   10 5 Rewrite 8.42  10 4 as  10 5.