Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Multiply. 1. 724  102 2. 837  10 3. 632.9  100 72,400 8,370 63,290

Problem of the Day A rope ladder is hanging from the back of a yacht. At 10:00 A.M., the water reaches the third step on the ladder. If the water rises the height of 2 steps every 2 hours, at what step would the water level be at 5:00 P.M.? Explain. the third, because the boat will rise with the water

Learn to write large numbers in scientific notation.

Vocabulary scientific notation

Additional Example 1A: Multiplying by Powers of Ten Find each product. 5,892  1,000 There are 3 zeros in 1,000. 5,892.000 To multiply, move the decimal 3 places right. = 5,892,000 Write 3 placeholder zeros.

Additional Example 1B: Multiplying by Powers of Ten Find each product. 47.75  10,000 There are 4 zeros in 10,000. 47.7500 To multiply, move the decimal 4 places right. = 477,500 Write 4 placeholder zeros.

Check It Out: Example 1A Find each product. 901  1,000 There are 3 zeros in 1,000. 901.000 To multiply, move the decimal 3 places right. = 901,000 Write 3 placeholder zeros.

Check It Out: Example 1B Find each product. 15.425  10,000 There are 4 zeros in 10,000. 15.4250 To multiply, move the decimal 4 places right. = 154,250 Write 4 placeholder zeros.

Scientific notation is a shorthand method that can be used to write large numbers. A number written in scientific notation has two numbers that are multiplied. 4.123  105 The first part is a number that is greater than or equal to 1 and less than 10. The second part is a power of 10.

Additional Example 2: Writing Numbers in Standard Notation Write 6,000,000 in scientific notation. 6,000,000 Move the decimal point 6 places left. The power of 10 is 6. 6,000,000 6,000,000 = 6  106

Check It Out: Example 2 Write 4,325,000 in scientific notation. Move the decimal point 6 places left. The power of 10 is 6. 4,325,000 4,325,000 = 4.325  106

You can write a large number written in scientific notation in standard form. Look at the power of 10 and move the decimal point that number of places to the right.

Additional Example 3: Writing Numbers in Standard From Write 6.2174  103 in standard form. 6.2174  103 The power of 10 is 3. 6.2174 Move the decimal point 3 places right. 6.2174  103 = 6,217.4

Check It Out: Example 3 Write 3.21975  103 in standard form. 3.21975  103 The power of 10 is 3. 3.21975 Move the decimal point 3 places right. 3.21975  103 = 3,219.75

Additional Example 4 Write the distance to the sun, 93,000,000 miles, in scientific notation. 93,000,000 Move the decimal point left to form a number that is greater than or equal to 1 and less than 10. Multiply that number by a power of ten. 93,000,000 The power of 10 is 7, because the decimal point is moved 7 places left. 9.3  107 The distance to the sun is 9.3  107.

Check It Out: Example 4 Write the distance 132,500 in scientific notation. 132,500 Move the decimal point left to form a number that is greater than or equal to 1 and less than 10. Multiply that number by a power of ten. 132,500 The power of 10 is 5, because the decimal point is moved 5 places left. 1.325  105 The distance is 1.325  105.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz Write each number in scientific notation. 1. 6,300 2. 70,400,000 Write each number in standard form. 3. 7.241  104 4. 8.2137  107 5. A Wall Street report indicated that a fast-moving stock had sold 3,295,000 shares. Write this number in scientific notation. 6.3  103 7.04  107 72,410 82,137,000 3.295  106

Lesson Quiz for Student Response Systems 1. Which of the following represents 9,400 in scientific notation? A. 9.4  102 B. 9.4  103 C. 94  102 D. 94  103

Lesson Quiz for Student Response Systems 2. Which of the following represents 5,328,000 in scientific notation? A. 5328  103 B. 532.8  103 C. 53.28  105 D. 5.328  106

Lesson Quiz for Student Response Systems 3. Which of the following represents 1.1132  105 in scientific notation? A. 11,132,000 B. 1,113,200 C. 111,320 D. 11,132

Lesson Quiz for Student Response Systems 4. Which of the following represents 7.9132  106 in scientific notation? A. 79,132 B. 791,320 C. 7,913,200 D. 79,132,000

Lesson Quiz for Student Response Systems 5. Jupiter is at a distance of 778,600,000 km from the sun. Identify this number in scientific notation. A. 7.786  108 B. 7.786  107 C. 7.786  106 D. 7.786  105