# 7N1 PLUS The Real Number System (rational and irrational)

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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) 7N3 Place rational and irrational numbers (approximations) on a number line and justify the placement of the numbers 7N17 Classify irrational numbers as non-repeating/non-terminating decimals Lesson 2 Contents

Number Systems Real Rational (fraction) Integer Irrational Whole
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

Name all of the sets of numbers to which the real number 17 belongs.
7N1 PLUS The Real Number System (rational and irrational) 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 2-1a

Name all of the sets of numbers to which the real number belongs.
7N1 PLUS The Real Number System (rational and irrational) Name all of the sets of numbers to which the real number belongs. Answer: Since , this number is an integer and a rational number. Example 2-1a

Name all of the sets of numbers to which the real number belongs.
7N1 PLUS The Real Number System (rational and irrational) 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. Example 2-1a

Name all of the sets of numbers to which the real number belongs.
7N1 PLUS The Real Number System (rational and irrational) 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 . Example 2-1a

Name all of the sets of numbers to which the real number belongs.
7N1 PLUS The Real Number System (rational and irrational) 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. Example 2-1a

Name all of the sets of numbers to which each real number belongs.
7N1 PLUS The Real Number System (rational and irrational) Name all of the sets of numbers to which each real number belongs. a. 31 b. c d. e. 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 2-1b

Replace  with <, >, or = to make a true statement.
7N1 PLUS The Real Number System (rational and irrational) Replace  with <, >, or = to make a true statement. Express each number as a decimal. Then graph the numbers. Example 2-2a

Answer: Since is to the left of 7N1 PLUS
The Real Number System (rational and irrational) Since is to the left of Answer: Example 2-2a

Order from least to greatest.
7N1 PLUS The Real Number System (rational and irrational) Order from least to greatest. Express each number as a decimal. Then compare the decimals. Example 2-2a

From least to greatest, the order is
7N1 PLUS The Real Number System (rational and irrational) Answer: From least to greatest, the order is Example 2-2a

a. Replace  with <, >, or = to make a true statement.
7N1 PLUS The Real Number System (rational and irrational) a. Replace  with <, >, or = to make a true statement. b. Order from least to greatest. Answer: > Answer: Example 2-2b

Solve . Round to the nearest tenth, if necessary.
7N1 PLUS The Real Number System (rational and irrational) 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. Answer: The solutions are 13 and –13. Example 2-3a

Solve . Round to the nearest tenth, if necessary.
7N1 PLUS The Real Number System (rational and irrational) 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. Answer: The solutions are 7.1 and –7.1. Example 2-3a

Solve each equation. Round to the nearest tenth, if necessary.
7N1 PLUS The Real Number System (rational and irrational) Solve each equation. Round to the nearest tenth, if necessary. a. b. Answer: 9 and –9 Answer: 4.9 and –4.9 Example 2-3b