rational numbers

63 Rational NumbersWarm-up1) 30% 0f $802) Find the mean: 20, 40, 50, 30, 10

3) Find the next three terms: 1, 2, 4, 8,__, __, __4) 1/9 of 7200

5) 2/3 = 8/x X = ____

6) (2.0 X 105) (3.0 X 106)

63 Rational Numbers

Remember: A rational number must be able to be expressed as a ratio / fraction.

63 Example 1

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

• Express 2/11 as an equivalent decimal and percent. Then express 2/11 as a decimal rounded to the thousandths place.

63 Example 2

• Express 16 2/3 % as a reduced fraction and as a decimal.

• Convert the percent to a fraction and decimal– 8 1/3 %

63 Example 3

• Arrange these numbers in order from least to greatest.– 4/5, 83 1/3%, 0.83

63 Example 4

• 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. The calculate the exact number of votes.

63 Fractions with Negative Exponents

• Recall that with fractions, we can reverse the position of the numerator and denominator to form the reciprocal. – Ex: ¾ 4/3– Ex: x/y y/x

• If the base of a negative exponent is a fraction, we make the exponent positive by replacing the fraction with its reciprocal.– Ex: (2/3)-4 (3/2)4

– Ex: (x/y)-n (y/x)n

63 Example 5

• Simplify: (1/3)-2

• Simplify: (1/2)-3