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But in the third place b has a zero whereas c has a 1.Īlso, c and a have the same digits in the first four places of their decimal representations but in the fifth place c has a zero and a has a 1. We observe that in the first two places of their decimal representations b and c have the same digits.

Thus, d is an irrational number such thatĬlearly, c is an irrational number as it has non-repeating and non-terminating decimal representation. Since b has a zero in the third place of decimal and c has a 1. Then, c is a rational number as it has a terminating decimal representation. But in the third place a has a 1 and b has a zero. Clearly, a and b are rational numbers such that a bĬonstruction of a rational number between a and b : As mentioned above, first two digits after the decimal point of a and b are the same. Hence required irrational number are 6 1/4 and 2 1/4 × 6 1/8Įxample 13: Find two irrational numbers between 0.12 and 0.13. These type of decimals are known as pure recurring decimals.įor Example: \(0.\overline \) = 2 1/4 × 6 1/8. A decimal in which all the digit after the decimal point are repeated.In a non terminating repeating decimal, there are two types of decimal representations

Step-4: Find a common divisor of the numerator and denominator and express the rational number to lowest terms by dividing its numerator and denominator by the common divisor.Ĭase II: When decimal representation is of non-terminating repeating nature.Write 1 in the denominator and put as many zeros on the right side of 1 as the number of digits in the decimal part of the given rational number. Step-3: Remove decimal point from the numerator.Step-2: Determine the number of digits in its decimal part.Conversion Of Decimal Numbers Into Rational Numbers Of The Form m/nĬase I: When the decimal number is of terminating nature.