Rational and Irrational Numbers 1.1 Rational and Irrational Numbers How do you express a rational number as a decimal and approximate the value of an irrational number?

Texas Essential Knowledge and Skills The student is expected to: Number and operations—8.2.B Approximate the value of an irrational number, including and square roots of numbers less than 225, and locate that rational number approximation on a number line. Mathematical Processes 8.1.D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

ADDITIONAL EXAMPLE 1 Write each fraction as a decimal. A. 0.4 B.

ADDITIONAL EXAMPLE 2 Find the two square roots of each number. A. 900 30, –30 B.

1.1 LESSON QUIZ 8.2.B 1. Write as a decimal: 2. Find the two square roots of . 3. Approximate to the nearest 0.05 without using a calculator: 3.65 4. Between which two whole numbers will be on a number line? 7 and 8

5. When you graph on a number line, will it be closer to 3 or to 4? Explain. It will be closer to 3; the value is approximately 3.14.

Write on the board and invite students to conjecture what the value might be. Have them check their conjectures by squaring. Invite them to suggest ways to estimate . As a hint, point out that 0.9 is close to 1.0, and so they might use that to help guide their estimates. Lead them to see that, since 0.92 is 0.81 and 1.02 is 1, the value of is greater than 0.9 and less than 1.0. Try squaring 0.95 to get 0.9025. A good estimate for is 0.95.

How do you express a rational number as a decimal and approximate the value of an irrational number? To express as a decimal, divide the numerator by the denominator. To approximate an irrational number, estimate a number between two consecutive perfect squares.