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Number System- Rational Numbers & Real Numbers Video Lecture - Class 9
FAQs on Number System- Rational Numbers & Real Numbers Video Lecture - Class 9
| 1. What are rational numbers and real numbers? |  |
Ans. Rational numbers are numbers that can be expressed as a fraction (ratio) of two integers, where the denominator is not zero. Real numbers, on the other hand, include all rational numbers along with irrational numbers, which cannot be expressed as a fraction and have non-recurring decimal representations.
| 2. How are rational numbers and real numbers different? | |
Ans. The main difference between rational numbers and real numbers lies in their definition and representation. Rational numbers can be expressed as fractions, whereas real numbers include both rational and irrational numbers. Rational numbers have repeating or terminating decimal representations, while irrational numbers have non-recurring, non-terminating decimals.
| 3. Can all rational numbers be represented as real numbers? | |
Ans. Yes, all rational numbers can be represented as real numbers. This is because rational numbers are a subset of real numbers. Every rational number can be written as a decimal, either terminating or repeating, which makes it a real number.
| 4. Are all real numbers rational numbers? | |
Ans. No, not all real numbers are rational numbers. Real numbers include both rational and irrational numbers. Irrational numbers cannot be expressed as a fraction of two integers and have non-terminating, non-recurring decimal representations. Examples of irrational numbers include square roots of non-perfect squares (such as √2 or √3) and constants like π and e.
| 5. How are rational and real numbers used in everyday life? | |
Ans. Rational and real numbers are used in various aspects of everyday life. Rational numbers are used in measurements, calculations, and comparisons involving fractions, ratios, and proportions. Real numbers, including irrational numbers, are used in fields like physics, engineering, and finance to represent continuous quantities, such as distances, time, temperature, and financial values. They are also used in everyday situations like estimating distances, measuring ingredients for recipes, and calculating interest rates on loans.
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