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Scientific Notation Learn to express large and small numbers in scientific notation.

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43210 In addition to 3, student will be able to go above and beyond by applying what they know about working with integer exponents. The student will be able to work with integer exponents. - Know and apply the properties of exponents. - Simplify numerical expressions with exponents. - Perform operations with scientific notation. With no help the student has a partial understanding of integer exponents. - Is able to use scientific notation to estimate very large or very small numbers. - Interpret scientific notation generated by technology. With help, the student may have a partial understanding of how to work with integer exponents. Even with help, the student is unable to work with integer exponents. Focus 11 - Learning Goal: The student will be able to work with integer exponents.

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An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about 0.00000003 centimeters across. The length of these numbers in standard notation makes them awkward to work with. Scientific notation is a shorthand way of writing such numbers.

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The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Helpful Hint In scientific notation the number of atoms in a penny is 2.0 10 22, and the size of each atom is 3.0 10 –8 centimeters across.

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135,000 1.35 100,000 Think: Move the decimal right 5 places. A. 1.35 10 5 1.35 10 5 10 = 100,000 5 Write the number in standard notation.

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0.0027 Think: Move the decimal left 3 places. B. 2.7 10 –3 Write the number in standard notation.

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C. –2.01 10 4 –20,100 Think: Move the decimal right 4 places. Write the number in standard notation.

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2,870,000,000 Think: Move the decimal right 9 places. D. 2.87 10 9 Write the number in standard notation.

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0.000019 Think: Move the decimal left 5 places. E. 1.9 10 –5 Write the number in standard notation.

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Translating Standard Notation to Scientific Notation Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative. 0.00709 Move the decimal to get a number between 1 and 10. 7.09 7.09 10 Set up scientific notation. Think: The decimal needs to move 3 places. 7.09 10 –3 = 0.00709 Write 0.00709 in scientific notation.

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Think: The decimal needs to move left to change 8.11 to 0.000811, so the exponent will be negative. 0.000811 Move the decimal to get a number between 1 and 10. 8.11 8.11 10 Set up scientific notation. Think: The decimal needs to move 4 places. Check 8.11 10 = 0.000811 –4 Write 0.000811 in scientific notation. So 0.000811 written in scientific notation is 8.11 10 –4.

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Lesson Quiz Write in standard notation. 1. 1.72 10 4 2. 6.9 10 –3 4. 57,000,000 17,200 0.0069 3. 0.0053 5.3 10 –3 5.7 10 7 Write in scientific notation. 5. A human body contains about 5.6 x 10 6 micro-liters of blood. Write this number in standard notation. 5,600,000

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