4-4 Scientific Notation Warm Up Order each set of numbers from least to greatest , 10, 10, , 8, 8, , 2, 2, , 5.2, 5.2, –1 –2 10, 10, 10, –1– , 8, 8, –2 13 –4 –6 –2 29 –1 5.2, 5.2, 5.2, –1–2 2, 2, 2, 2 31 –4–6

4-4 Scientific Notation Learn to express large and small numbers in scientific notation and to compare two numbers written in scientific notation.

4-4 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.

4-4 Scientific Notation 135,000 Think: Move the decimal right 5 places   = 100,000 5 Example 1A: Translating Scientific Notation to Standard Notation Write the number in standard notation. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Helpful Hint

4-4 Scientific Notation Think: Move the decimal left 3 places. 2.7  10 –3 Write the number in standard notation. Example 1B: Translating Scientific Notation to Standard Notation Continued

4-4 Scientific Notation 2.01  ,100 Think: Move the decimal right 4 places  10 4 Example 1C: Translating Scientific Notation to Standard Notation Continued Write the number in standard notation.

4-4 Scientific Notation 2,870,000,000 Think: Move the decimal right 9 places   10 9 Write the number in standard notation. Example 2A

4-4 Scientific Notation Think: Move the decimal left 5 places. 1.9  10 –5 1.9  10 –5 Write the number in standard notation. Example 2B

4-4 Scientific Notation 5.09  10 8 Write the number in standard notation. Example 2C 509,000,000 Think: Move the decimal right 8 places.

4-4 Scientific Notation

4-4 Scientific Notation To write scientific notation for numbers greater than or equal to 1 and less than 10, use a 0 exponent = 5.63 x 10°. Writing Math

4-4 Scientific Notation Example 3: Translating Standard Notation to Scientific Notation Think: The decimal needs to move left to change 7.09 to , so the exponent will be negative Think: The decimal needs to move 3 places to get a number between 1 and  10 Set up scientific notation. Check 7.09  10 –3 = 7.09  = Write in scientific notation. So written in scientific notation is 7.09  10 –3.

4-4 Scientific Notation Example 4 Think: The decimal needs to move left to change 8.11 to , so the exponent will be negative Think: The decimal needs to move 4 places to get a number between 1 and  10 Set up scientific notation. Check 8.11  10 = 8.11  = –4 Write in scientific notation. So written in scientific notation is 8.11  10 –4.

4-4 Scientific Notation Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

4-4 Scientific Notation Lesson Quiz: Part I Write each number in standard notation   10 – ,000,000 17,  10 –3 5.7  10 7 Write each number in scientific notation. 5. Order the numbers from least to greatest. T 2  10 –4, 9  10 –5, 7  10 –5 7  10 –5, 9  10 –5, 2  10 –4

4-4 Scientific Notation Lesson Quiz: Part II 6. A human body contains about 5.6  10 6 microliters of blood. Write this number in standard notation. 5,600,000

4-4 Scientific Notation 1. Write the number in standard notation. 3.2  10 3 A. 32 B. 320 C D Lesson Quiz for Student Response Systems

4-4 Scientific Notation 2. Write the number in standard notation. 0.9  10 –3 A. 0.9 B C D Lesson Quiz for Student Response Systems

4-4 Scientific Notation 3. Write the number in scientific notation A  10 –1 B  10 –1 C  10 –2 D  10 –3 Lesson Quiz for Student Response Systems

4-4 Scientific Notation 4. Write the number in scientific notation. 13,432 A  10 4 B  10 –4 C  10 –4 D  10 4 Lesson Quiz for Student Response Systems