Five-Minute Check (over Lesson 10–1)

Then/Now

New Vocabulary

Key Concept: Irrational Number

Example 1: Classify Real Numbers

Example 2: Compare Real Numbers

Example 3: Order Real Numbers

Example 4: Solve Equations

Example 5: Real-World Example: Use Real Numbers to Solve Problems

Over Lesson 10–1

A.

B.

C. 6

D. 7

Over Lesson 10–1

A. 9

B. 10

C. 11

D. 12

Over Lesson 10–1

A. –9

B. –8

C. 7

D. 8

Over Lesson 10–1

A. 7

B. 8

C. 9

D. 10

Over Lesson 10–1

A. 12 cm

B. 14 cm

C. 15 cm

D. 20 cm

The area of a square is 200 cm2. Estimate the length of a side of the square.

Over Lesson 10–1

A. A

B. B

C. C

D. D

You have already compared fractions and decimals. (Lesson 3–1)

• Identify and compare numbers in the real number system.

• Solve equations by finding square roots.

• irrational numbers

• real numbers

Classify Real Numbers

A. Name all of the sets of numbers to which the real number 0.246 belongs. Write whole, integer, rational, or irrational.

Answer: This decimal is a rational number because its

digits repeat. It is equivalent to

Classify Real Numbers

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

B. Name all of the sets of numbers to which the real number belongs. Write whole, integer, rational, or irrational.

Classify Real Numbers

C. Name all the sets of numbers to which the real number –7.25 belongs. Write whole, integer, rational, or irrational.

Answer:

Classify Real Numbers

D. Name all of the sets of numbers to which the real number belongs. Write whole, integer, rational, or irrational.

Answer:

A. rational number

B. irrational number

C. integer, rational number

D. whole number

A. Name all the sets of numbers to which the real number 0.380 belongs. Write whole, integer, rational, or irrational.

A. rational number

B. irrational number

C. integer, rational number

D. whole number

B. Name all the sets of numbers to which the real

number belongs. Write whole, integer, rational,

or irrational.

A. rational

B. whole, integer, rational

C. whole, integer

D. irrational

C. Name all the sets of numbers to which –2.25 belongs. Write whole, integer, rational, or irrational.

A. rational

B. whole, integer, rational

C. whole, integer

D. irrational

D. Name all the sets of numbers to which belongs. Write whole, integer, rational, or irrational.

Compare Real Numbers

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

Compare Real Numbers

A. <

B. >

C. =

D. none of the above

Order Real Numbers

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

Order Real Numbers

A.

B.

C.

D.

Solve Equations

A. Solve w 2 = 169. Round to the nearest tenth, if

necessary.

w 2 = 169

Write the equation.

Answer: The solutions are 13 and –13.

Definition of square root.

w = 13 or w = –13

Solve Equations

B. Solve r 2 = 50. Round to the nearest tenth, if

necessary.

r 2 = 50

Write the equation.

Answer: The solutions are approximately 7.1 and –7.1.

Definition of square root.

Use a calculator.

A. 8

B. 8 and –8

C. 9

D. 9 and –9

A. Solve the equation m2 = 81. Round to the nearest tenth, if necessary.

A. 4.8 and –4.8

B. 4.9

C. 4.9 and –4.9

D. 5 and –5

B. Solve the equation h2 = 24. Round to the nearest tenth, if necessary.

Use Real Numbers to Solve Problems

Write the formula.

Replace R with 6.4 and A with 40.

Use Real Numbers to Solve Problems

Answer: The wingspan is 16 feet.

Multiply each side by 40.

Consider only the positivesquare root.

Simplify.

A. 7.1 ft

B. 9.9 ft

C. 14 ft

D. 98 ft