The Real Number System

Define an integer.

• An integer is a whole number that can be positive, negative, or zero, but does not include fractions or decimals.

• An integer is a number that can be expressed as a fraction of two integers.

• An integer is a decimal number that can be positive or negative.

• An integer is a number that is always positive.

What is an irrational number?

• A number that can be expressed as a simple fraction.

• A number whose decimal representation terminates.

• A number that cannot be expressed as a simple fraction; its decimal representation goes on forever without repeating.

• A whole number that is not a fraction.

Classify the number -4.2.

• A) -4.2 is an irrational number because it cannot be expressed as a fraction.

• B) -4.2 is a whole number because it is negative.

• C) -4.2 is a rational number because it can be expressed as -42/10.

• D) -4.2 is an integer because it is a negative number.

What are whole numbers?

• Negative integers including -1, -2, -3, ...

• Non-negative integers including 0 (0, 1, 2, 3, ...)

• All integers including both positive and negative numbers

• Only positive integers (1, 2, 3, ...)

Classify the number 0.04769165821735...

• 0.04769165821735... is a rational number because it can be expressed as a fraction.

• 0.04769165821735... is an irrational number because it has a non-repeating, non-terminating decimal.

• 0.04769165821735... is an integer because it is less than 1.

• 0.04769165821735... is a whole number because it is positive.

Classify the number 4.2.

• 4.2 is an irrational number because it cannot be expressed as a fraction.

• 4.2 is a whole number because it is not a decimal.

• 4.2 is a rational number because it can be expressed as 42/10.

• 4.2 is an integer because it is a positive number.

Is 0 a whole number?

• Yes, 0 is considered a whole number.

• No, 0 is not a whole number.

• 0 is a negative number.

• 0 is a decimal number.

Classify the number -78.

• -78 is a natural number.

• -78 is an integer, a rational number, and a real number.

• -78 is an irrational number.

• -78 is a whole number.

What is a rational number?

• A number that can be expressed as a fraction of two integers, where the denominator is not zero.

• A number that cannot be expressed as a fraction.

• A number that is always an integer.

• A number that has an infinite number of decimal places.

Classify the number 4/3.

• 4/3 is an irrational number because it cannot be expressed as a fraction.

• 4/3 is a rational number because it is a fraction of two integers.

• 4/3 is a whole number because it is greater than 1.

• 4/3 is an imaginary number because it has a real part.