LESSON

How can you use scientific notation to express very large quantities?

Scientific Notation with PositivePowers of 102.1

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

1.4 ×108

ADDITIONAL EXAMPLE 2Write 7.8 × 109 in standard notation.

7,800,000,000

2.1 LESSON QUIZ8.2.C

642,000,000,000,000,000,000,000 kg

The approximate mass of Mars is 6.42 × 1023 kilograms. Write this mass in standard notation.

1.

4 × 107 krill

An adult blue whale can eat about 40,000,000 krill a day. Write this number in scientific notation.

2.

7 × 100

Write 7 in scientific notation.3.

Write 1.0 × 105 in standard notation and in words.

4.

100,000; one hundred thousand

Is 10.2 × 105 written in scientific notation? Explain.

5.

No; the first number is not greater than 1 and less than 10.

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

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.

Ask students to consider the three numbers and compare each pair.

3.2 × 103 8.7 × 103 2.4 × 104

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.