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Rational Numbers and Rational Cuts Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET

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FAQs on Rational Numbers and Rational Cuts Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET

1. What are rational numbers?
Ans. Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero. They can also be represented on a number line.
2. What are rational cuts?
Ans. Rational cuts, also known as Dedekind cuts, are a way to define irrational numbers. A rational cut divides the set of rational numbers into two non-empty subsets, such that every number in the first subset is less than every number in the second subset.
3. How can rational numbers be represented geometrically?
Ans. Rational numbers can be represented geometrically on a number line. Each rational number corresponds to a point on the line, where the distance of the point from the origin represents the magnitude of the number.
4. What is the difference between rational numbers and irrational numbers?
Ans. Rational numbers can be expressed as fractions and can be written as terminating or repeating decimals. Irrational numbers, on the other hand, cannot be expressed as fractions and have non-repeating, non-terminating decimal representations.
5. Can rational numbers be negative?
Ans. Yes, rational numbers can be negative. A rational number can be positive, negative, or zero. It can be written with a negative sign before the fraction or as a negative numerator.
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