Positive Rational Number Positive Rational Number Any number that can be expressed as the ratio x/y where x and y are both positive integers. [Technically, they could both be negative, but not one of each. Rational Numbers are those numbers which can be represented in the form of p/q where p and q are Real Numbers and q cannot be zero. We generally use “q� to represent rational numbers in mathematical world. They can be represented in two ways- either in fraction or in decimal forms and contain the Set of integers. If a/b and b/c are two rational numbers then the two rational numbers are equal only if ac=bd. Performing any operation using rational numbers is just like using Fractions. Some important points on rational numbers: 1. All the rational numbers are subset of real numbers or we can say all rational numbers lie in real line. 2. Countless rational numbers lie between two rational numbers. 3. There can be infinite numbers of rational numbers between two integers. 4. Any Integer can be represented as rational number. 5. Rational numbers are countable numbers as we can easily count them. Rational numbers are very densely populated as I mentioned above that there can be infinite rational number between two integers. We can also find many rational numbers between two numbers. We can perform many Operations on Rational Numbers like addition, subtraction, division and multiplication. Know More About :- Co-ordinate Geometry
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Is Zero a Rational Number If we have two integers ‘m’ and ‘n’ that can be written in the form of rational number mn provided ‘n’ is not equal to zero. We cannot have a rational form in which the denominator is equal to zero. If the numerator of a rational number is not zero and the denominator of the expression comes very close to zero then the value of the fraction becomes very large and may approach infinity as the denominator approaches zero. The rational expression of having both the numerator and the denominator equaling zero would be the same as any other number. 00 = 2 or 0 x 2 = 0 and we can also see that 00 = 9 or 0 x 9 = 0. Representation of Rational Numbers on a Number In any number line, zero occupies the middle place. The positive rational numbers lie to the right of zero and the negative rational numbers lie to the left of zero. Mark zero and name that point as O. Now mark +1 to the right and -1 to the left of zero equally spaced from zero. The mid-point between O and +1 is 12 and the mid-point between 0 and -1 is −12. Similarly we can mark as many rational numbers on the number line as possible. To mark a rational number on a number line, divide each of the unit lengths on it into as many divisions as in the denominator of the rational number and then move as many steps as is mentioned in the numerator of the rational number. Let us try to plot 4/7 on the number line.
Observe that each unit is divided into 7 equal parts.
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