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Learn to convert between standard form and scientific notation with examples and practice exercises. Understand the significance of scientific notation and perform operations effectively.
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Scientific Notation Objective: I will convert between standard form and scientific notation MAFS.8.EE.1.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (MP.2, MP.5, MP.6)
10 , 10 , 10 , 10 0 4 –2 –1 8 , 8 , 8 , 8 0 2 3 –2 2 , 2 , 2 , 2 1 3 –6 –4 5.2 , 5.2 , 5.2 , 5.2 2 9 –2 –1 Do Now Order each set of numbers from least to greatest. 1. 10 , 10 , 10 , 10 4 0 –2 –1 2. 8 , 8 , 8 , 8 2 3 0 –2 3. 2 , 2 , 2 , 2 3 1 –6 –4 4. 5.2 , 5.2 , 5.2 , 5.2 2 9 –1 –2
Scientific Notation Vocabulary: • Scientific notation: is a way of writing numbers that are too big or too small to be conveniently written in decimal form • Fact 1: The number , for arbitrarily large positive integer , is a big number in the sense that given a number (no matter how big it is) there is a power of 10 that exceeds . • Fact 2: The number , for arbitrarily large positive integer , is a small number in the sense that given a positive number (no matter how small it is), there is a (negative) power of that is smaller than .
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 centimeter 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 Numbers written in scientific notation are written as two factors. One factor is a number greater than or equal to 1 and less than 10. The other factor is a power of 10.
Scientific Notation • Example 1:The average ant weighs about 0.0003 grams. • Observe that this number is less than 1 and is very small. We want to express this number as a power of 10. We know that , so we must need a power of 10 that is less than zero. Based on our knowledge of decimals and fractions, we can rewrite the weight of the ant as , which is the same as . Our work with the laws of exponents taught us that . Therefore, we can express the weight of an average ant as grams.
5 10 = 100,000 1.35 10 5 Helpful Hint A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Scientific Notation Write the number in standard notation. 1.35 105 1.35 100,000 Think: Move the decimal right 5 places. 135,000
1 2.7 10–3 –3 10 = 1000 1 2.7 1000 Scientific Notation Write the number in standard notation. 2.7 10–3 2.7 1000 Divide by the reciprocal. 0.0027 Think: Move the decimal left 3 places.
–2.01 104 4 10 = 10,000 –2.01 10,000 Scientific Notation Write the number in standard notation. –2.01 104 –20,100 Think: Move the decimal right 4 places.
8.11 10 –4 Scientific Notation Write 0.000811 in scientific notation. 0.0008ᵒ11
Scientific Notation A pencil is 18.7 cm long. If you were to lay 10,000 pencils end-to-end, how many millimeters long would they be? Write the answer in scientific notation. 1 centimeter = 10 millimeters 18.7 centimeters = 187 millimeters Multiply by 10. 187 mm 10,000 Find the total length. Multiply. 1,870,000 mm
Scientific Notation A certain cell has a diameter of approximately 5 x 10-3 meters. A second cell has a diameter of 5.11 x 10-3 meters. Which cell has a greater diameter? and 5.11 ˃ 5; second cell 10-3 = 10-3
