Irrational Numbers

An irrational number is a real number that cannot be expressed as a fraction of two integers and also cannot be written as a terminating or repeating decimal. In other words, irrational numbers cannot be written in the form a/b, where a and b are integers and b is not equal to 0.

Examples of irrational numbers include the square root of non-perfect squares, such as √2, √3, and √5. Another famous irrational number is π (pi), which represents the ratio of the circumference of a circle to its diameter.

When irrational numbers are expressed as decimals, they go on forever without repeating. For example, the decimal representation of √2 is 1.4142135623730950488016887242097… and it never repeats or terminates.

It's important to note that not all real numbers are irrational. Rational numbers, which can be expressed as fractions, are a subset of real numbers that include integers, fractions, and terminating or repeating decimals.

Understanding irrational numbers is important in mathematics, as they play a crucial role in various mathematical concepts and applications, such as geometry, trigonometry, and calculus.

Overall, irrational numbers are an essential part of the real number system, and they introduce unique and non-repeating patterns that contribute to the richness and diversity of numbers in mathematics.

◂Math Worksheets and Study Guides Third Grade. Fractions

Fractions and Decimals

Worksheet/Answer key

Fractions and Decimals

Create And Print more Fractions worksheets with Comparing Fractions, Equivalent Fractions, and Simplifying Fractions

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Grade 3 Curriculum Focal Points (NCTM)

Number and Operations: Developing an understanding of fractions and fraction equivalence

Students develop an understanding of the meanings and uses of fractions to represent parts of a whole, parts of a set, or points or distances on a number line. They understand that the size of a fractional part is relative to the size of the whole, and they use fractions to represent numbers that are equal to, less than, or greater than 1. They solve problems that involve comparing and ordering fractions by using models, benchmark fractions, or common numerators or denominators. They understand and use models, including the number line, to identify equivalent fractions.