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Scientific Notation Warm-up 1. Sign Social Contract. 2. Take out your 3 subject spiral. Number the pages. 3. Make table of contents on the first page of the spiral. (see white board). 4. Pass out textbook Volume 1. Do Launch the Lesson on Pg.49 Interactive Notebook 1. 2. 3. 4. Leave first 2 pages for table of contents. Pg. 1 – Syllabus Pg. 2 – 6 weeks calendar and TEKS Pg. 3 – Warm up/HW on left side, notes on right side Scientific Notation Scientific Notation Learn to express large and small numbers in scientific notation and to compare two numbers written in scientific notation. Vocabulary scientific notation Scientific Notation An ordinary quarter contains about 97,700,000,000,000,000,000,000 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. Scientific Notation To express any number in scientific notation, write it as the product of a number between 1 and 10 and a power of ten Scientific Notation Helpful Hint A number less than 1 will have a negative exponent when written in scientific notation. A number MORE than 1 will have a positive exponent when written in scientific notation. STANDARD TO SCIENTIFIC 97,700,000,000,000,000,000,000 Step 1: Move the decimal until you get to a number between 1 and 10. Step 2: Count the number of places you moved the decimal and put it as a power of 10. Answer__________________ STANDARD TO SCIENTIFIC 0.00000003 Step 1: Move the decimal until you get to a number between 1 and 10. Step 2: Count the number of places you moved the decimal and put it as a power of 10. Answer__________________ Scientific Notation Translating Standard Notation to Scientific Notation Write 0.00709 in scientific notation. Write 0.000811 in scientific notation. Scientific Notation Translating Standard Notation to Scientific Notation Write 436000 in scientific notation. Write 378000 in scientific notation. Scientific Notation Translating Scientific Notation to Standard Notation Look at the exponent Positive power: Move the decimal to the right Negative power: Move the decimal to the left. Scientific Notation Scientific Notation Translating Scientific Notation to Standard Notation Write the number in standard notation. 1.35 105 Write the number in standard notation. 2.7 10–3 PRACTICE Convert the following numbers to Scientific Notation. 1. .0005389 2. 405,389,000 3. 1,903,000 4. .0328701 PRACTICE Convert from Scientific Notation to Standard Form. 1. 2. 3. 4. -5 10 5.836 x 9 8.301 x 10 -4 6.1 x 10 1 7.54 x 10 Write in scientific notation: 1) 245,000,000 2) 0.0000000832 Write in standard notation: 3) 4.23 x 105 4) 6.426 x 10-4 Applying Scientific Notation The diameter of an atom is about 0.000002 of an inch. Express this number in scientific notation. Solar System The distance from the sun to the planet Neptune is about 2,762,000,000 miles. Express this number in scientific notation. Micro-Biology The biologist viewed the germ in the microscope. He recorded the measurement on his chart. He wrote 4.63 x 10-4 of an inch. How is this number expressed in standard form? Applying Scientific Notation Venus is 6.724 x 107 miles from the sun. Express this number in standard form. Which number is less: 7.2 x 107 or 9.9 x 105? Which number is greater: 3.5 x 104 or 2.1 x 106? Use <, >, = to answer 4.34 x 104 4.5 x 104 6.2 x 10-7 6.8 x 10-8 8.84 x 106 8.141 x 108 Use <, >, = to answer 5.9 x 1011 5.88 x 1012 2.2 x 10-9 2.77 x 10-8 7.4 x 105 7.44 x 105 Put the numbers in order from least to greatest. -2 10 1.5 x 1.2 x 10-2 -3 5.85 x 10 2.3 x 10-2 5.5 x 106 Lesson Quiz: Part I Write each number in standard notation. 1. 1.72 104 17,200 2. 6.9 10–3 0.0069 Write each number in scientific notation. 3. 0.0053 5.3 10–3 4. 57,000,000 5.7 107 5. Order the numbers from least to greatest. T 2 10–4, 9 10–5, 7 10–5 7 10–5, 9 10–5, 2 10–4