1. Bell Work: Solve the inequality and graph the solution on a number line. 2x – 5 ≤ 3

2. Answer: x ≤ 4

3. Lesson 63: Rational Numbers, Non-Terminating Decimals and Percents, Fractions with Negative Exponents

4. Recall that every rational number can be expressed as a ratio of two integers. Converting the ratio to a decimal number results in a decimal that terminates (ends) or does not terminate but has repeating digits.

5. Terminating: 1/8 = 0. 125 Non-Terminating but repeating: 1/11 = 0

6. We do not perform computations with a decimal number that has a bar over the repetend. Instead we use the fraction equivalent, or we round the decimal number to an appropriate number of decimal places.

7. Example: Express 2/3 as an equivalent decimal and percent
Example: Express 2/3 as an equivalent decimal and percent. Then express 2/3 as a decimal rounded to the thousandths place.

8. Answer: Decimal: 0.6 Percent: 66 2/3% Rounded: 0.667
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9. Example: Express 16 2/3% as a reduced fraction and as a decimal.

10. Answer: 16 2/3% = 16 2/ /3 x 1/100 = 1/6 1/6 = 0.16
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11. Practice: Arrange these numbers in order from least to greatest

12. Answer: 4/5, 0.83, 83 1/3%

13. Practice: The incumbent received 41 2/3% of the 1260 votes cast in the town council election. Describe how to estimate the number of votes the incumbent received. Then calculate the exact number of votes.

14. Answer: 40% of 1260 will be a little more than 500
Answer: 40% of 1260 will be a little more than /3% = 125/300 = 5/12 5/12 x 1260 = 525 votes

15. Recall that the negative exponent indicates the reciprocal of the positive power of the base. x = 1 3 = 1 x 3 -n n

16. Also recall that with fractions we reverse the position of the numerator and the denominator to form the reciprocal. the reciprocal of x/y = y/x

17. If the base of a negative exponent is a fraction, we make the exponent positive by replacing the fraction with its reciprocal. (x) = (y) (y) (x)
-n n

18. Example: Simplify (1) (3) -2

19. Answer: 9

20. HW: Lesson 63 #1-25