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SCIENTIFIC NOTATION

You will learn: how to express numbers in scientific notation and standard form how to find the products and quotients of numbers expressed in scientific notation. SCIENTIFIC NOTATION. WARM UP. 1. Simplify : . 2. 3k – 5 = 7k - 21. 3. . 4. .

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SCIENTIFIC NOTATION

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  1. You will learn: • how to express numbers in scientific notation and standard form • how to find the products and quotients of numbers expressed in scientific notation SCIENTIFIC NOTATION

  2. WARM UP 1. Simplify: 2. 3k – 5 = 7k - 21 3. 4. Express the area of the triangle as a single exponential expression: 2q 6q³ 5.

  3. SCIENTIFIC NOTATION http://www.youtube.com/watch?v=H578qUeoBC0 When dealing with very large or very small numbers, keeping track of place value can be difficult. For this reason, numbers such as these are often expressed in scientific notation. A number is expressed in scientific notation when it is written as a product of a factor and a power of 10. The factor must be greater than or equal to 1 and less than 10. A number in scientific notation is written as where 1 ≤ a < 10 and n is an integer.

  4. The following examples show one way of expressing a number that is written in scientific notation in its decimal or standard notation. Look carefully at the relationship between the power of 10 and the position of the decimal point in standard notation of the number. • 6.59 x = 6.59 x 10,000 = 65,900 (the decimal point moved 4 places to the right) • 4.81 x = 4.81 x = 4.81 x 0.000001 = 0.00000481 • (the decimal point moved 6 places to the left) • These examples suggest the following rules for expressing a number written in scientific notation in standard form and a number written in standard form in scientific form:

  5. Scientific to standard notation Use these steps to express a number of the form in standard notation. Determine whether n>0, or n<0. If n>0, move the decimal point in a to the right n places. If n<0, move the decimal point in a to the left n places. Add zeros, decimal point, and/or commas as needed to indicate place value. Examples: 2.45 x = 2.45 x 100,000,000 = 245,000,000 (n = 8 so move the decimal point 8 times to the right) 3 x = 3 x = 0.00003 (n = -5 so move the decimal point 5 places to the left.

  6. STANDARD TO SCIENTIFIC NOTATION • Use these steps to express a number in scientific notation: • 1. Move the decimal point so that it is to the right of the first nonzero digit. The result is a decimal number a. • Observe the number of places n and the direction in which you moved the decimal point. • If the decimal point moved to the left, write as . • If the decimal point moved to the right, write as a· . • Examples: • 30,500,000 → 3.0500000 x (move the decimal point 7 places to the left. • 30,500,000 = 3.05 x (a = 3.05 and n = 7) • 0.000781 → 00007.81 x (move the decimal point 4 places to the right. • 0.000781 = 7.81 x (a = 7.81 and n = -4)

  7. Using Scientific Notation. . . . The following information shows chocolate and candy sales during a recent holiday: Candy Canes: $120 million Chocolate: $300 million All candy: $1.45 billion Express the sales of candy canes, chocolates, and all candy in standard notation. 2. Write each of these sales figures in scientific notation.

  8. Express the number in each statement in standard notation: There are 2 x stars in the Andromeda Galaxy. The center of the moon is 2.389 x miles away from the center of the earth. The mass of a proton is 1.67265 x kilograms. The mass of an electron is 9.1095 x kilograms.

  9. Problems to solve: In the 1930’s the Indian physicist, Subrahmanyan Chandrasekhar and others predicted the existence of neutron stars. These stars can have a density of 10 billion tons per teaspoonful. Express this density in scientific notation. 2. The unit of measure for counting molecules is a mole. One mole of a substance is the amount that contains about 602,214,299,000,000,000,000,000 molecules. Write this number in scientific notation.

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