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Introduction |
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The sets of numbers which every student must remember are:
The set of natural numbers, The set of whole numbers, The set of integers, The set of rational numbers, The set of irrational numbers, Set of Real Numbers, Consecutive integers, Factor, Common factor, Prime numbers, Composite number, Prime factors, Numbers prime to each other, Rule of Divisibility, Fraction, Types of fractions, Simplification of fractions. |
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Rational Numbers |
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The rational numbers can be expressed as terminating or recurring decimals.
Decimal fraction has denominator as 10 or a power of 10.
A recurring decimal is denoted by placing dots or a bar over recurring digits. |
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Irrational Numbers |
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Numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring.
We can obtain infinite number of irrationals between two irrational numbers. |
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Surd |
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If K is not a perfect nth power of any number, then  is called a surd of the nth order.
A surd is always an irrational number. |
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Real Numbers |
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The union of the set of rational numbers and irrational numbers forms the set of real numbers.
(i) For every real number, there is a corresponding point on the number line.
(ii) For every point on the number line, there exists a real number. |
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Conjugate surds |
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 is the conjugate surd of  . Their product is a rational number, |
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Summary |
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1. Problems involving rational numbers are simplified using 'BODMAS' rule. |
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2. A rational number can be represented in the decimal form. |
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3. When a rational number is represented as a decimal, it will be either a terminating decimal or a recurring decimal. |
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4. All rational and irrational numbers can be marked on the number line. |
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5. Numbers with surds in the denominator are supposed to be simplified by rationalising their denominators.
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