Scientific Notation with Positive Powers of 10 2.1 Scientific Notation with Positive Powers of 10 How can you use scientific notation to express very large 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.A Apply mathematics to problems arising in everyday life, society, and the workplace.

ADDITIONAL EXAMPLE 1 The average distance from Earth to Mars is about 140,000,000 miles. Write this distance in scientific notation. 1.4 ×108

ADDITIONAL EXAMPLE 2 Write 7.8 × 109 in standard notation. 7,800,000,000

2.1 LESSON QUIZ 8.2.C 1. The approximate mass of Mars is 6.42 × 1023 kilograms. Write this mass in standard notation. 642,000,000,000,000,000,000,000 kg 2. An adult blue whale can eat about 40,000,000 krill a day. Write this number in scientific notation. 4 × 107 krill 3. Write 7 in scientific notation. 7 × 100

4. Write 1.0 × 105 in standard notation and in words. 100,000; one hundred thousand 5. Is 10.2 × 105 written in scientific notation? Explain. No; the first number is not greater than 1 and less than 10.

by comparing the coefficient Ask students to consider the three numbers and compare each pair. 3.2 × 103 8.7 × 103 2.4 × 104 When comparing two numbers written in scientific notation, should students compare the coefficient or the power of 10 first? the power of 10 Which pair of numbers have the same power of 10? 3.2 × 103 and 8.7 × 103 When the power of 10 is the same, how do you compare the numbers? by comparing the coefficient

no Ask students to consider the three numbers and compare each pair. 3.2 × 103 8.7 × 103 2.4 × 104 When the power of 10 is different, do you need to compare the coefficient? no Have students write their own set of rules to describe how to compare two numbers written in scientific notation.

How can you use scientific notation to express very large quantities? Sample answer: Write the large quantity as the product of a number greater than or equal to 1 and less than 10 and a power of 10.