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Whole Numbers, Integers, and Rational Numbers (Definition, Examples and Worksheets)

Grade 6 Math Worksheets

In the vast realm of mathematics, numbers play a fundamental role in representing quantities, measurements, and relationships. Understanding the different types of numbers is crucial for building a strong mathematical foundation.

In this article, we explore the concepts of whole numbers, integers, and rational numbers, providing clear definitions, illustrative examples, and interactive worksheets to solidify your understanding.

rational number is one that is a part of a whole denoted as a fraction, decimal or a percentage. It is a number which cannot be expressed as a fraction of two integers (or we can say that it cannot be expressed as a ratio).

 

For instance, let’s consider the square root of 3. It is irrational and cannot be expressed by two integers.

It is an irrational number because it cannot be denoted as a fraction with just two integers.

rational and irrational numbers

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Whole Numbers, Integers and Natural Numbers - Grade 6 Math Worksheet PDF

This is a free printable / downloadable PDF worksheet with practice problems and answers. You can also work on it online.

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Integers and Rational numbers

They are the numbers you usually count and they will continue upto infinity.

Whole numbers are all natural numbers including 0.

Example: 0, 1, 2, 3, 4…

Integers are all whole numbers and their negative sides too.

Example….. -6,-5,-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6…

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 Check Point

 

  1. Arrange the following integers in the ascending order:
  1.  -17, 1, 0, -15, 16,8, 33, 6
  2. -44, -66, 0, 23, 41, 55, 15, 11, 10, -1, -2
  1. Identify whether the following is rational or irrational number.
  1. 0.5
  2. \sqrt{200}
  3. \sqrt{121}
  4. 9.0
  5. 5

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Ordering of Rational Numbers – FAQs

What are whole numbers?

Whole numbers are non-negative integers that include zero and extend infinitely in the positive direction. They are used for counting objects or representing quantities that are not fractional or decimal.

What are integers?

Integers are numbers that include both positive and negative whole numbers, including zero. They extend the number line in both directions and are used to represent values that involve gain and loss, such as temperature changes, financial transactions, or positions on a coordinate plane.

What are rational numbers?

Rational numbers are numbers that can be expressed as a ratio of two integers. They include fractions and decimals that either terminate or repeat. Rational numbers are written in the form of a/b, where a and b are integers, and b is not equal to zero.

How do rational numbers differ from irrational numbers?

Rational numbers can be expressed as fractions or decimals that terminate or repeat, whereas irrational numbers cannot be expressed as fractions and have decimal representations that neither terminate nor repeat. Irrational numbers include square roots of non-perfect squares, such as √2 or π.

Can all integers be rational numbers?

No, not all integers are rational numbers. While all whole numbers are rational, integers that are not whole numbers, such as negative integers or non-zero positive integers, are also rational. However, integers that cannot be expressed as a ratio of two integers, such as √2 or -π, are considered irrational numbers.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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