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

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

Number SystemsNumber SystemsRealReal Rational (fraction)Rational (fraction)

IrrationalIrrationalIntegerInteger

WholeWhole

NaturalNatural

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.

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.

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

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

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 .

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.

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. 4.375

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

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

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

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

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

Since is to the left ofAnswer:

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

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

Order from least to greatest.

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

Answer: From least to greatest, the order

is

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:

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

Solve . Round to the nearest tenth, if necessary.

Answer: The solutions are 13 and –13.

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)

Answer: The solutions are 7.1 and –7.1.

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)

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

a.

b.

Answer: 9 and –9

Answer: 4.9 and –4.9

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