Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Scientific Notation Information Page Astronomy Session 5 What Is Scientific Notation? Scientific notation is a shorthand method for writing very large or very small numbers. • An astronomer uses scientific notation to express very large numbers, such as distances between planets or stars. For example, the distance from our Sun to the nearest star (Proxima Centauri) is almost 25.8 trillion miles. This number can be written in two ways: Standard number form: 25,800,000,000,000 mi • Scientific notation: 2.58 x 1013 mi A physicist or chemist uses scientific notation to express very small numbers, such as the sizes of atoms or molecules. For example, a hydrogen atom measures 12 ten-billionths of a meter across. This number can also be written in two ways: Standard number form: .00000000012 m Scientific notation: 1.2 x 10-10 m Writing a Number in Scientific Notation A number written in scientific notation has two parts: the base* and the power of ten. • The base is obtained by moving the decimal point until you have a number between one and 10. Move the decimal point 13 places to the left to obtain a base of 2.58. Move the decimal point 10 places to the right to obtain a base of 1.2. • The power of ten is the number of times you must multiply the base by 10 to return to the original number. It consists of the number 10 and an exponent – a small number above and to the right of the 10. The exponent is obtained by counting how many places you had to move the decimal point to get a base between one and 10. For 25,800,000,000,000, the exponent is +13. Because the number is larger than one, you moved the decimal point to the left; therefore, the exponent is positive. For .00000000012, the exponent is -10. Because the number is less than one, you moved the decimal point to the right; therefore, the exponent is negative. Orders of Magnitude Sometimes powers of 10 are called orders of magnitude. This phrase is usually used to indicate whether a particular calculation or estimate is within the correct range of values. For example: Estimate of a person’s height: 6 feet 60 feet (correct estimate) (high by one order of magnitude, or one power of ten) Estimate of the distance from Earth to the Sun: 93,000,000 miles 93,000 miles (correct estimate) (low by three orders of magnitude) * Note: If no base is given, the base is assumed to be one; for example, 106 = 1 x 106. © 2001‐2009 Pitsco Education 1 MO•0501•0409•04 Scientific Notation Information Page Astronomy Session 5 Table of Selected Powers of Ten Power of Ten 12 10 1011 109 106 103 102 101 100 10-1 10-2 10-3 10-4 10-6 10-9 10-10 10-12 10-14 Long Number 1,000,000,000,000 100,000,000,000 1,000,000,000 1,000,000 1,000 100 10 1 0.1 0.01 0.001 0.0001 0.000001 0.000000001 0.0000000001 0.000000000001 0.00000000000001 Place Designation trillions hundred billions billions millions thousands hundreds tens ones tenths hundredths thousandths ten thousandths millionths billionths ten billionths trillionths hundred trillionths Prefix Example of Unit Using Prefix Real-World Example* teraradius of solar system gigamegakilohectodeka- kilometer decicentimilli- decimeter centimeter millimeter micronano- micrometer nanometer pico- picometer radius of Earth height planes fly height of building height of child paper length paper thickness radius of atom radius of nucleus * For measurements of length in meters, these measurements of objects or distances are within one power of ten (one order of magnitude) of the power described in the given row of the table. Calculating with Scientific Notation Multiplication: • Multiply the bases and add the exponents. • Adjust the resulting number so that the base is between one and 10. • Example: (4 x 104) x (8 x 1010) = 32 x 1014 = 3.2 x 1015 Division: • Divide the bases and subtract the exponents. • Adjust the resulting number so that the base is between one and 10. • Example: 20 x 109 = 4 x 104 5 x 105 Addition or Subtraction: • Write both numbers in the same power of 10. • Add or subtract the base numbers. • Example: 5.4 x 106 + 3.2 x 109 = .0054 x 109 + 3.2 x 109 = 3.2054 x 109 © 2001‐2009 Pitsco Education 2 MO•0501•0409•04