Irrational Numbers: Introduction and Property

Irrational Number Introduction 

The numbers that cannot be expressed as the ratio of two integers are called irrational numbers. Irrational numbers are in contradiction to rational numbers. Rational numbers can be denoted as a fraction of two numbers but irrational numbers cannot be denoted in a fraction form using two integers. 

The irrational numbers can be decimal numbers, but the decimal part of an irrational number does not terminate which means the number has no definite value. For example, the decimal representation of 2/3 = 0.6666…, continues but does not give any exact value. So it can be said that if a number has no finite value or fixed number of digits, it can be called an irrational number. 

The irrational and rational numbers together form the set of real numbers. If the set of real numbers is denoted by A and rational numbers are denoted by B, then irrational numbers can be expressed as A-B.

Irrational Number Properties

  • Irrational numbers are not fractions or integers.
  • The decimal part of an irrational number is non-terminating.
  • Irrational numbers are real numbers with approximate values but not finite values.
  • The sum of an irrational number and a rational number will be an irrational number. 
  • The product of an irrational number and any nonzero rational number will be an irrational number. 
  • Irrational numbers are not perfect squares of any integer.
  • Two irrational numbers when added, subtracted, multiplied, or divided with any other irrational number, the result can be either rational or irrational numbers. 

Mathematics Worksheets 

Mathematics is a subject that can be learned best by solving practice problems. Mathematics worksheets are designed for this purpose to cover practice problems on different mathematics topics suitable for different grades of students. The worksheets are prepared in a well-organized manner to guide students about the step-by-step learning mechanism. Worksheets allow students to approach a problem with conceptual understanding, solve on their own, and become aware of their mistakes if any. Mathematics worksheets consist of different varieties of problems required to be solved in a logical way that helps students to develop their mathematical ability and confidence. It also helps students to learn about time management as they have to complete assignments within the time limit. Math worksheets have been found quite beneficial and help in effective learning for students. With more practice, the students will be able to develop a strong foundation on mathematical concepts. 

Solving worksheet problems of different types on different topics help students to boost their logical thinking and reasoning skills. These worksheets can enhance the students’ confidence and help them score well in exams. Math worksheets also play a very important role in improving the speed and accuracy of students. The use of visual aids and application-based exercises for students of lower age groups helps to understand the concepts clearly. Math worksheets can be available for the entire range of topics that the students are learning in their particular grade. Mathematics worksheets are carefully prepared by highly qualified teaching faculty to ensure that it complements the regular learning activities by giving the opportunity to practice more on problem-solving exercises.

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Teachers prepare mathematics worksheets that consist of a variety of questions like multiple choice questions, fill in the blanks, true or false, problem sums, matching questions, and others. The aim is to make students competent in looking at the assigned problems from different perspectives and solve in their own way and pace. The basic objective is to help students in active learning by creating an engaging experience that requires concentration, conceptual clarity, and a logical approach. More practice of worksheets would advance students towards perfection and accuracy. Practicing the assignments and monitoring the results help students to track their progress and work on improvement.

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