Classify Real Numbers

Pick the vocabulary word that best matches the following definition:

Any number that can be written as a fraction. These numbers in decimal form terminate or repeat.

• Real Numbers

• Rational Numbers

• Irrational Numbers

• Natural Numbers

• Integers

Answer explanation

The definition describes numbers that can be expressed as fractions, which is the characteristic of rational numbers. They can be represented in decimal form as either terminating or repeating, distinguishing them from irrational numbers.

Pick the vocabulary word that best matches the following definition:

These numbers consist of all rational numbers and irrational numbers.

• Whole Numbers

• Natural Numbers

• Rational Numbers

• Real Numbers

• Integers

Answer explanation

The definition includes all rational and irrational numbers, which are collectively known as real numbers. Whole numbers and natural numbers are subsets of real numbers, while rational numbers do not include irrationals.

Pick the vocabulary word that best matches the following definition:

These numbers include counting numbers as well as 0.

• Whole Numbers

• Real Numbers

• Irrational Numbers

• Natural Numbers

• Integers

Answer explanation

Whole numbers are defined as non-negative integers, which include 0. Natural numbers, on the other hand, start from 1 and do not include 0. Therefore, the correct answer is Whole Numbers.

Pick the vocabulary word that best matches the following definition:

These numbers are all counting numbers.

• Natural Numbers

• Integers

• Rational Numbers

• Irrational Numbers

• Whole Numbers

Answer explanation

Natural numbers are whole numbers starting from 1 and do not include zero. They are also known as counting numbers, making 'Natural Number' the best match for the definition provided.

Pick the vocabulary word that best matches the following definition:

These numbers can be positive, negative, or zero, but cannot be decimals or fractions.

• Whole Numbers

• Natural Numbers

• Irrational Numbers

• Integers

• Rational Numbers

Answer explanation

The definition describes numbers that can be positive, negative, or zero, which aligns with integers. Whole numbers are only non-negative, natural numbers are positive only, and real numbers include decimals and fractions.

Pick the vocabulary word that best matches the following definition:

These numbers cannot be written as a/b, where a and b are both integers and b is not equal to zero. These numbers in decimal form do not repeat or terminate.

• Rational Numbers

• Integers

• Natural Numbers

• Irrational Numbers

• Real Numbers

Answer explanation

Irrational numbers cannot be expressed as a fraction of two integers and their decimal form neither repeats nor terminates, distinguishing them from rational numbers, which can be expressed as a/b.

Chose the most specific group to classify the numbers below.

{... -3, -2, -1, 0, 1, 2, 3...}

• Rational Numbers

• Whole Numbers

• Natural Numbers

• Integers

Answer explanation

The set {... -3, -2, -1, 0, 1, 2, 3...} includes all positive and negative whole numbers, as well as zero. This defines the group of Integers, making it the most specific classification compared to the other options.

Chose the most specific group to classify the numbers below.

{ 0, 1, 2, 3, 4, ...}

• Real Numbers

• Integers

• Whole Numbers

• Natural Numbers

Answer explanation

The set {0, 1, 2, 3, 4, ...} includes all non-negative integers, which defines Whole Numbers. While it also fits Real Numbers and Integers, Whole Numbers is the most specific classification.

• Rational Numbers

• Irrational Numbers

• Real Numbers

• Integers

Answer explanation

The numbers \(\sqrt{2}\) and \(\pi\) are irrational, meaning they cannot be expressed as fractions. The number 7.123875438345973... is also irrational as it is non-repeating and non-terminating. Thus, the most specific group is Irrational Numbers.

• Integers

• Irrational Numbers

• Natural Numbers 

• Whole numbers

Answer explanation

The numbers -√9, 14/2, -3/3, and √49 simplify to -3, 7, -1, and 7 respectively. All these values are integers, making 'Integers' the most specific group to classify them.