Making Sense of the Definition and Rational Numbers Examples Rational Irrational and Real Numbers

Which of the following sentences is true? Select all answers that apply.

• Irrational numbers often include a symbol, such as square root or pi.

• Whole numbers and natural numbers both begin with zero.

• Integers include all natural numbers, whole numbers, and their opposites.

• All rational numbers are integers.

Answer explanation

Irrational numbers can not be expressed as a ratio of two integers and are thus often written with a symbol or radical.

Integers are positive and negative counting numbers and zero.

Which of the following fractions has the smallest value?

• 3/4

• 3/7

• 1/2

• 4/9

Answer explanation

3/7 is less than half because half of 7 is 3.5. The decimal equivalent is about 0.43.

Tags

CCSS.4.NF.A.2

Students were asked to name point B. Zoe wrote that B equals -2.4, Julio responded that it equals -2 ¼, Sage said that it equaled -3 ¾ and Kaitlyn said that Zoe and Julio were both correct because the numbers were equivalent. Which student was correct in their response?

• Zoe

• Julio

• Sage

• Kaitlyn

Answer explanation

Point B is between -2 and -3. It is halfway between -2 and -2 ½ which means it is located at -2 ¼.

Tags

CCSS.6.NS.C.6C

Order the following numbers from greatest to least: -2, ½, 0.76, 5, √2, π.

• -2, ½, 0.76, √2, π, 5

• -2, 0.76, ½, √2, π, 5

• 5, π, √2, 0.76, -2, ½

• 5, π, √2, 0.76, ½, -2

Answer explanation

The largest number is 5, which rules out answer choices C and D. The biggest issue here might be deciding which is larger: π or √2. It is important to know that a good estimate for π is ≈ 3; it is good to know that √2, the square root of 2, is some irrational number slightly bigger than 1. So π > √2 and so far, we have: 5, π, √2. 0.76 is close to 0.75 or 3/4, which is bigger than 1/2. -2 is the smallest, the only number less than 0. So, the correct order is 5, π, √2, 0.76, 1/2, -2.

Tags

CCSS.8.NS.A.2

True or False: The set of irrational numbers is a subset of rational numbers.

• True

• False

• A

• B

• C

• D

• A

• B

• C

• D

A rational number can be written as terminating or repeating decimals.

• true

• false

Tags

CCSS.7.NS.A.2D

CCSS.8.NS.A.1

The Venn diagram shows the relationship among several sets of numbers. Indicate whether the following numbers are rational or irrational. \sqrt[]{3} ​ ​: ​​ ​ (a)   ​ \sqrt[]{9} : ​ ​ (b)  

• Irrational

• Rational

• Both Rational & Irrational

According to the Real Number Chart, CAN "Irrational Numbers be "Rational Numbers"?

• No, because they are completely separate boxes.

• Yes, because they are all Real Numbers.