2. Lesson Menu Main Idea and New Vocabulary Key Concept:Scientific Notation Example 1:Express Large Numbers in Standard Form Example 2:Express Small Numbers in Standard Form Example 3:Express Numbers in Scientific Notation Example 4:Express Numbers in Scientific Notation Example 5:Compare Numbers in Scientific Notation

3. Main Idea/Vocabulary Express numbers in scientific notation and in standard form. scientific notation

4. Key Concept

5. Example 1 Express Large Numbers in Standard Form Express 3.56 × 10 5 in standard form. Answer: 356,000 3.56 × 10 5 = 3.56 × 100,00010 5 = 100,000 = 356,000Move the decimal point 5 places.

6. Example 1 CYP A.0.414 B.4.14 C.41.4 D.414 Express 4.14  10 2 in standard form.

7. Example 2 Express 1.4 × 10 –6 in standard form. Express Small Numbers in Standard Form Answer: 0.0000014 1.4 × 10 –6 = 1.4 × 0.00000110 –6 = 0.000001 = 0.0000014Move the decimal point 6 places.

8. Example 2 CYP A.0.000213 B.0.00213 C.0.0213 D.0.213 Express 2.13 × 10 –4 in standard form.

9. Example 3 Express Numbers in Scientific Notation Express 268,000 in scientific notation. Answer: 2.68 × 10 5 268,000 = 2.68 × 10,000The decimal point moves 5 places. = 2.68 × 10 5 The exponent is positive.

10. Example 3 CYP A.2.3 × 10 2 B.2.3 × 10 3 C.23.0 × 10 3 D.0.23 × 10 4 Express 2,300 in scientific notation.

11. Example 4 Express 0.00000028 in scientific notation. Express Numbers in Scientific Notation Answer: 2.8 × 10 –7 0.00000028 = 2.8 × 0.0000001The decimal point moves 7 places. = 2.8 × 10 –7 The exponent is negative.

12. Example 4 CYP A.0.3 × 10 –5 B.3.0 × 10 –5 C.30 × 10 –5 D.300 × 10 –5 Express 0.00003 in scientific notation.

13. Example 5 Compare Numbers in Scientific Notation PLANETS Earth has an average radius of 6.38 × 10 3 kilometers. Mercury has an average radius of 2.44 × 10 3 kilometers. Which planet has the greater average radius? 6.38 > 2.446.38 × 10 3 > 2.44 × 10 3 Answer: So, Earth has the greater average radius.

14. Example 5 CYP A.Sound travels faster at sea level. B.Sound travels faster at 20,000 feet. C.Sound travels the same speed at sea level and at 20,000 feet. SOUND At sea level, the speed of sound is about 1.225  10 3 kilometers per hour. At 20,000 feet, the speed of sound is 1.062  10 3 kilometers per hour. Does sound travel faster at sea level or at 20,000 feet?