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| Rational Numbers |
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| We have defined rational numbers as those which can be expressed as fractions: |
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| We now define decimal fractions. |
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| The rational numbers can be expressed as terminating or recurring decimals. |
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| Decimal fraction has denominator as 10 or a power of 10. |
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| 2.793 represents 2 units, seven-tenths, nine-hundredths and three-thousandths or using fraction notation: |
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(a)  |
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(b)  |
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(a)  |
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(b)  |
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| Hence we state the classical definition of rational numbers: |
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Find a rational number between two rational numbers  |
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| To obtain the required number, add numerators and denominators as shown below: |
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Ans:  |
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Find three rational numbers between  |
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i.e.,  |
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 are three rational numbers between  |
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| We can obtain infinite number of rationals between two given rational numbers. |
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| A recurring decimal is denoted by placing dots or a bar over recurring digits. |
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| Express the following recurring decimals as equivalent fractions: |
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(a)  |
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(b)  |
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(c)  |
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| (a) Let x = 0.4444…… |
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Multiply both sides by 10 ( one digit is recurring) |
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(b) Let x =  |
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Multiply both sides by 100 ( two digits are recurring) |
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| We can find equivalent fraction for recurring decimal |
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(c) Let x =  |
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