HOW DO WE CLASSIFY AND USE REAL NUMBERS?

0-2: Real Numbers

0-2: Real Numbers

Natural Numbers: 1, 2, 3, …Whole Numbers: 0, 1, 2, 3, …Integers: …, -2, -1, 0, 1, 2, …Rational Numbers

Decimals that terminate (have an end) Decimals that repeat Fractions where both numerator and denominator are

integersIrrational Numbers

Decimals that don’t have a repeating pattern Square roots that aren’t perfect squares

0-2: Real Numbers

Square Root: One of two equal factors of a number E.g. One square root of 64 (written as ) is 8,

because 8 ● 8 = 64. The positive square root is called the principle square root. Another square root of 64 is -8, since -8 ● -8 = 64.

A perfect square is any number where the principle square root is also a rational number. 64 is a perfect square since its principle square roots are 8 2.25 is a perfect square since its principle square root is

1.5

64

0-2: Real Numbers

Name the set or sets of numbers to which each real number belongs 5/22

Because both 5 and 22 are integers (and because 5/22 = 0.22727272… which is a repeating decimal), this is a rational number

Because the square root of 81 is 9, this is a natural

number, a whole number, an integer, and a rational number

Because the square root of 56 is 7.48331477…, which

does not repeat or terminate, this is an irrational number

81

56

0-2: Real Numbers

Graph each set of numbers on a number line. Then order the numbers from least to greatest. {5/3, -4/3, 2/3, -1/3}

5/3 ≈ 1.66666667 -4/3 ≈ -1.33333333 2/3 ≈ 0.666666667 -1/3 ≈ -0.33333333

{-4/3, -1/3, 2/3, 5/3}

0 0.5 1 1.5 20–0.5–1–1.5–2

0-2: Real Numbers

Graph each set of numbers on a number line. Then order the numbers from least to greatest. { , 4.7, 12/3, 4 1/3}

sqrt(20) ≈ 4.47213595… 4.7 = 4.7 12/3 = 4 4 1/3 ≈ 4.33333333

{12/3, 4 1/3, , 4.7}

20

1 1.5 2 2.5 3 3.5 4 4.5 5

20

0-2: Real Numbers

Any repeating decimal can be written as a fraction Write 0.7 as a fraction Let N = 0.7

Since one digit repeats, multiply each side by 10 If two digits repeat, multiply each side by 100. If three repeating digits multiply each side by 1000, etc.

10N = 7.7 Subtract N from 10N to eliminate the repeating part

10N = 7.7- N = 0.7

9N = 7 Divide both sides by 9 N = 7/9

0-2: Real Numbers

You can simplify fractional square roots by simplifying the numerator and denominator separately Simplify

You can estimate roots that are not perfect squares Estimate to the nearest whole number

9 is a perfect square (3 ● 3) 16 is a perfect square (4 ● 4) Because 15 is closer to 16, the best estimate for is 4

4121

4121

211

15

15

0-2: Real Numbers

Assignment Page P10 Problems 1 – 35, odds