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Lesson 2 Contents. 7N1 PLUS. The Real Number System (rational and irrational). 7 N 1  Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, and irrational numbers)

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Lesson 2 contents

Lesson 2 Contents

7N1 PLUS

The Real Number System (rational and irrational)

7N1 Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, and irrational numbers)

7N2   Recognize the difference between rational and irrational numbers (e.g., explore different approximations of π)

7N3Place rational and irrational numbers (approximations) on a number line and justify the placement of the numbers

7N17Classify irrational numbers as non-repeating/non-terminating decimals


Number systems

Real

Rational (fraction)

Integer

Irrational

Whole

Number Systems

Natural

Natural – counting numbers beginning with 1, 2, 3, …

Whole – counting numbers beginning with 0, 1, 2, 3, …

Integer – All the whole numbers and their opposites {…, –3, –2, –1, 0, 1, 2, 3, …}

Rational – all numbers that can be written as a ratio (fraction)

Irrational – a decimal that never ends and never repeats

Real– all numbers that can be put on a number line


Example 2 1a

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-1a

Name all of the sets of numbers to which the real number 17 belongs.

Answer:This number is a natural number, a whole number, an integer, and a rational number.


Example 2 1a1

Name all of the sets of numbers to which the real number belongs.

Answer:Since , this number is an integer and a rational number.

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-1a


Example 2 1a2

Name all of the sets of numbers to which the real number belongs.

Answer:Since , this number is a natural number, a whole number, an integer, and a rational number.

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-1a


Example 2 1a3

Name all of the sets of numbers to which the real number belongs.

Answer:This repeating decimal is a rational number because it is equivalent to.

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-1a


Example 2 1a4

Name all of the sets of numbers to which the real number belongs.

Answer:It is not the square root of a perfect square so it is irrational.

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-1a


Example 2 1b

Name all of the sets of numbers to which each real number belongs.

a.31

b.

c.4.375

d.

e.

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-1b

Answer:natural number, whole number, integer, rational number

Answer:integer, rational number

Answer:rational number

Answer:natural number, whole number, integer, rational number

Answer:irrational number


Example 2 2a

Replace  with <, >, or = to make a true statement.

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-2a

Express each number as a decimal. Then graph the numbers.


Example 2 2a1

Since is to the left of

Answer:

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-2a


Example 2 2a2

Order from least to greatest.

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-2a

Express each number as a decimal. Then compare the decimals.


Example 2 2a3

From least to greatest, the orderis

Answer:

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-2a


Example 2 2b

a.Replace  with <, >, or = to make a true statement.

b.Orderfrom least to greatest.

Answer:

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-2b

Answer:>


Example 2 3a

Solve . Round to the nearest tenth, if necessary.

Write the equation.

Take the square root of each side.

Find the positive and negative square root.

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-3a

Answer:The solutions are 13 and –13.


Example 2 3a1

Solve . Round to the nearest tenth, if necessary.

Write the equation.

Take the square root of each side.

Find the positive and negative square root.

Use a calculator.

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-3a

Answer:The solutions are 7.1 and –7.1.


Example 2 3b

Solve each equation. Round to the nearest tenth, if necessary.

a.

b.

7N1 PLUS

The Real Number System (rational and irrational)

Example 2-3b

Answer:9 and –9

Answer:4.9 and –4.9


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