Real Numbers and Their Properties from "summary" of NCERT Class 10 Mathematics Solutions by JagranJosh
Real numbers include all rational numbers and irrational numbers. Rational numbers are numbers that can be expressed as a ratio of two integers, whereas irrational numbers cannot be expressed as a ratio of two integers. The set of real numbers is denoted by the symbol R. Real numbers can be represented on the number line. The distance between two points on the number line is called the absolute value. The absolute value of a real number is always greater than or equal to zero. Real numbers have certain properties that help us perform operations on them. The properties of real numbers include closure property, commutative property, associative property, distributive property, additive identity property, multiplicative identity property, additive inverse property, multiplicative inverse property, and the property of 0. These properties help us simplify expressions and solve equations involving real numbers. The closure property states that the sum or product of two real numbers is also a real number. The commutative property states that the order of real numbers can be changed without affecting the result of addition or multiplication. The associative property states that the grouping of real numbers can be changed without aff...
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