Scientific Notation, Exams of Science education

Download Scientific Notation and more Exams Science education in PDF only on Docsity! Scientific Notation Section 7-1 Part 2 Goals Goal •  To write numbers in scientific notation and standard form. •  To compare and order numbers using scientific notation. Powers of 10 •  You can find the product of a number and a power of 10 by moving the decimal point of the number. –  If the exponent is positive, move the decimal point to the right. –  If the exponent is negative, move the decimal point to the left. •  You may need to write zeros to the right or left of the number in order to move the decimal point. A. 14 x 104 Multiply. 14.0 0 0 0 Since the exponent is a positive 4, move the decimal point 4 places to the right. 140,000 B. 3.6 x 10-5 0 0 0 0 3.6 Since the exponent is a negative 5, move the decimal point 5 places to the left. 0.000036 Example: Multiplying by Powers of 10 A. 2.5 x 105 Multiply. 2.5 0 0 0 0 Since the exponent is a positive 5, move the decimal point 5 places to the right. 250,000 B. 10.2 x 10-3 0 10.2 Since the exponent is a negative 3, move the decimal point 3 places to the left. 0.0102 Your Turn: 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. Example: Recognizing Scientific Notation Is the number written in scientific notation? Explain. 1.  53 ⨯  104 2.  3.42 ⨯  10-7 3.  0.35 ⨯  102 4.  9.6 ⨯  100 No, 53 is not less than 10 Yes No, 0.35 is not greater than or equal to 1 No, 100 is not in power of 10 form Your Turn: Is the number written in scientific notation? Explain. 1.  8.15 ⨯  10-6 2.  12.9 ⨯  108 3.  1.003 ⨯  107 4.  0.0045 ⨯  10-32 Yes No, 12.9 is greater than 10 Yes No, 0.0045 is not greater than or equal to 1 Think: The number is greater than 1, so the exponent will be positive. B. 23,000,000,000 Think: The decimal needs to move 10 places to get a number between 1 and 10. 2.3 x 1010 Write the number in scientific notation. So 23,000,000,000 written in scientific notation is 2.3 x 1010. Example: Writing Numbers in Scientific Notation Think: The number is less than 1, so the exponent will be negative. A. 0.000811 Think: The decimal needs to move 4 places to get a number between 1 and 10. 8.11 x 10 -4 Write the number in scientific notation. So 0.000811 written in scientific notation is 8.11 x 10–4. Your Turn: Think: The number is greater than 1, so the exponent will be positive. B. 480,000,000 Think: The decimal needs to move 8 places to get a number between 1 and 10. 4.8 x 108 Write the number in scientific notation. So 480,000,000 written in scientific notation is 4.8 x 108. Your Turn: 1.35000 135,000 Think: Move the decimal right 5 places. A. 1.35 x 105 1.35 x 10 5 Write the number in standard form. Example: Writing a Number in Standard Form 0002.7 Think: Move the decimal left 3 places. 2.7 x 10–3 B. 2.7 x 10–3 Write the number in standard form. 0.0027 Example: Writing a Number in Standard Form 2.870000000 Think: Move the decimal right 9 places. A. 2.87 x 109 2.87 x 10 9 Write the number in standard form. 2,870,000,000 Your Turn: A star has a diameter of approximately 5.11 x 103 kilometers. A second star has a diameter of 5 x 104 kilometers. Which star has a greater diameter? 5.11 x 103 5 x 104 Compare the exponents. The second star has a greater diameter. Notice that 3 < 4. So 5.11 x 103 < 5 x 104 Your Turn: Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. Step 2 Order the numbers that have the same power of 10 Example: Ordering Numbers in Scientific Notation Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. Step 2 Order the numbers that have the same power of 10 2 x 10-12, 4 x 10-3, 5.2 x 10-3, 3 x 1014, 4.5 x 1014, 4.5 x 1030 Your Turn: