Scientific Notation with Negative Powers of 10 2.2 Scientific Notation with Negative Powers of 10 How can you use scientific notation to express very small quantities?

Texas Essential Knowledge and Skills The student is expected to: Number and operations—8.2.C Convert between standard decimal notation and scientific notation. Mathematical Processes 8.1.D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

ADDITIONAL EXAMPLE 1 The weight of one of the smaller species of butterflies was measured at 0.0007 ounces. Write the weight of this butterfly in scientific notation. 7.0 × 10–4 ounces

ADDITIONAL EXAMPLE 2 A single atom of oxygen has a mass of 2.66 × 10–23 grams. Write 2.66 × 10–23 in standard notation. 0.0000000000000000000000266

2.2 LESSON QUIZ 8.2.C 1. The weight of an ant is about 1.7 ×10–5 pounds. Write 1.7 × 10–5 in standard notation. 0.000017 2. A bee sting delivers about 0.00005 grams of venom. Write this number in scientific notation. 5 × 10–5 3. Write 0.77 in scientific notation. 7.7 × 10–1

4. Write 1.0 × 10–3 in standard notation and in words. 0.001; one thousandth 5. Is 0.1 × 10–4 written in scientific notation? Explain. No; the first number is not greater than 1 and less than 10.

Have students write 0. 008 and 800 in scientific notation Have students write 0.008 and 800 in scientific notation. Notice that both of these numbers have two zeros that are essential (since 0.008 can be written as .008). Do both exponents have the same absolute value when the numbers are written in scientific notation? Explain. Sample answer: No; 0.008 = 8.0 × 10–3 and 800 = 8.0 × 102. When you move the decimal to the left, the 8 counts as one place. When you move to the right, the 8 is not included in the count of the number of moves.

How can you use scientific notation to express very small quantities? Write the small quantity as the product of a number greater than or equal to 1 and less than 10 times a power of 10 with a negative exponent.