1. Evaluating Algebraic Expressions 4-5 Scientific Notation NS1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10), compare rational numbers in general. California Standards

2. Evaluating Algebraic Expressions 4-5 Scientific Notation The table shows relationships between several powers of 10. Each time you divide by 10, the exponent in the power decreases by 1 and the decimal point in the value moves one place to the left. Each time you multiply by 10, the exponent in the power increases by 1 and the decimal point in the value moves one place to the right.

3. Evaluating Algebraic Expressions 4-5 Scientific Notation You can find the product of a number and a power of 10 by moving the decimal point of the number. You may need to write zeros to the right or left of the number in order to move the decimal point.

4. Evaluating Algebraic Expressions 4-5 Scientific Notation A. 14  10 4 Multiply. 14.0 0 0 0 Since the exponent is a positive 4, move the decimal point 4 places to the right. Additional Example 1: Multiplying by Powers of Ten 140,000 B. 3.6  10 5 0 0 0 0 3.6 Since the exponent is a negative 5, move the decimal point 5 places to the left. 0.000036

5. Evaluating Algebraic Expressions 4-5 Scientific Notation A. 2.5  10 5 Multiply. 2.5 0 0 0 0 Since the exponent is a positive 5, move the decimal point 5 places to the right. Check It Out! Example 1 250,000 B. 10.2  10 3 0 10.2 Since the exponent is a negative 3, move the decimal point 3 places to the left. 0.0102

6. Evaluating Algebraic Expressions 4-5 Scientific Notation Powers of 10 are used when writing numbers in scientific notation. Scientific notation is a way to express numbers that are very large or very small. Numbers written in scientific notation are expressed as 2 factors. One factor is a number greater than or equal to 1. The other factor is a power of 10.

7. Evaluating Algebraic Expressions 4-5 Scientific Notation Additional Example 2: Writing Numbers in Scientific Notation Think: The number is less than 1, so the exponent will be negative. A. 0.00709 Think: The decimal needs to move 3 places to get a number between 1 and 10. 7.09  10 3 Write the number in scientific notation. So 0.00709 written in scientific notation is 7.09  10 –3.

8. Evaluating Algebraic Expressions 4-5 Scientific Notation Additional Example 2: Writing Numbers in Scientific Notation Think: The number is greater than 1, so the exponent will be positive. B. 23,000,000,000 Think: The decimal needs to move 10 places to get a number between 1 and 10. 2.3  10 10 Write the number in scientific notation. So 23,000,000,000 written in scientific notation is 2.3  10 10.

9. Evaluating Algebraic Expressions 4-5 Scientific Notation Check It Out! Example 2 Think: The number is less than 1, so the exponent will be negative. A. 0.000811 Think: The decimal needs to move 4 places to get a number between 1 and 10. 8.11  10 4 4 Write the number in scientific notation. So 0.000811 written in scientific notation is 8.11  10 –4.

10. Evaluating Algebraic Expressions 4-5 Scientific Notation Check It Out! Example 2 Think: The number is greater than 1, so the exponent will be positive. B. 480,000,000 Think: The decimal needs to move 8 places to get a number between 1 and 10. 4.8  10 8 Write the number in scientific notation. So 480,000,000 written in scientific notation is 4.8  10 8.

11. Evaluating Algebraic Expressions 4-5 Scientific Notation 1.35000 135,000 Think: Move the decimal right 5 places. A. 1.35  10 5 1.35  10 5 Additional Example 3: Reading Numbers in Scientific Notation Write the number in standard form.

12. Evaluating Algebraic Expressions 4-5 Scientific Notation 0002.7 Think: Move the decimal left 3 places. 2.7  10 –3 B. 2.7  10 –3 Write the number in standard form. Additional Example 3: Reading Numbers in Scientific Notation 0.0027

13. Evaluating Algebraic Expressions 4-5 Scientific Notation 2.870000000 Think: Move the decimal right 9 places. A. 2.87  10 9 2.87  10 9 Write the number in standard form. Check It Out! Example 3 2,870,000,000

14. Evaluating Algebraic Expressions 4-5 Scientific Notation 000001.9Think: Move the decimal left 5 places. 1.9  10 –5 B. 1.9  10 –5 Write the number in standard form. Check It Out! Example 3 0.000019

15. Evaluating Algebraic Expressions 4-5 Scientific Notation A certain cell has a diameter of approximately 4.11  10 -5 meters. A second cell has a diameter of 1.5  10 -5 meters. Which cell has a greater diameter? 4.11  10 -5 1.5  10 -5 Compare the exponents. Additional Example 4: Comparing Numbers in Scientific Notation Compare the values between 1 and 10. The first cell has a greater diameter. 4.11 > 1.5 Notice that 4.11  10 -5 > 1.5  10 -5.

16. Evaluating Algebraic Expressions 4-5 Scientific Notation A star has a diameter of approximately 5.11  10 3 kilometers. A second star has a diameter of 5  10 4 kilometers. Which star has a greater diameter? 5.11  10 3 5  10 4 Compare the exponents. Check It Out! Example 4 The second star has a greater diameter. Notice that 3 < 4. So 5.11  10 3 < 5  10 4