**Identifying sets for real world situations :**

Real numbers can be used to represent real-world quantities. Highways have posted speed limit signs that are represented by natural numbers such as 55 mph. Integers appear on thermometers. Rational numbers are used in many daily activities, including cooking.

For example, ingredients in a recipe are often given in fractional amounts such as 2/3 cup flour.

**Example 1 : **

Identify the set of numbers that best describes the situation given below. Explain your choice.

"The number of people wearing glasses in a room"

**Answer : **

The set of whole numbers best describes the situation. The number of people wearing glasses may be 0 or a counting number.

**Example 2 : **

Identify the set of numbers that best describes the situation given below. Explain your choice.

"The circumference of a flying disk has a diameter of 8, 9, 10, 11, or 14 inches"

**Answer : **

The set of irrational numbers best describes the situation. Each circumference would be a product of π and the diameter, and any multiple of π is irrational.

**Example 3 : **

Identify the set of numbers that best describes the situation given below. Explain your choice.

"The amount of water in a glass as it evaporates"

**Answer : **

Real numbers ; the amount can be any number greater than 0.

**Example 4 : **

Identify the set of numbers that best describes the situation given below. Explain your choice.

"The number of seconds remaining when a song is playing, displayed as a negative number"

**Answer : **

Possible answer : Real numbers ; the number of seconds left can be any number less than 0, depending on the display device.

**Example 5 : **

Identify the set of numbers that best describes the situation given below. Explain your choice.

"The change in the value of an account when given to the nearest dollar"

**Answer : **

Integers ; the change can be a whole dollar amount and can be positive, negative, or zero.

**Example 6 : **

Identify the set of numbers that best describes the situation given below. Explain your choice.

"The markings on a standard ruler"

**Answer : **

Rational numbers ; the ruler is marked every 1/16 th inch.

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