1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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