Is 2.9 A Rational Number Is 2.9 A Rational Number A rational number is always represented as fraction i.e. in the form of p/q, where p and q are integers and q is not equal to zero.The set of all rational numbers is denoted by Q. So every integer is a rational number as q is equal to 1. The decimal expansion of a rational number is terminating or repeating,for eg. 3.345,5.87654 are some of the examples showing that the rational numbers terminate after a finite number of digits and the rational number 3.33333... is showing repetition of a finite squence of digits over and over. The numbers which are not rational are called irrational numbers.They are non terminating and non repeating.They include π,e and √2. Examples: √2=1.414213562.... e=4.113250379... π=3.141592654... The above mentioned numbers are all irrational numbers as they never terminate and repeat again and again. Know More About Velocity and acceleration vectors of Planar curves worksheet
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And there are many more such numbers that are not rational so are called irrational. Question:Is 2.9 A Rational Number? Answer:Yes. Because its decimal expansion terminates after 9 and it can also be represented as fraction. Since 29/10=2.9 There are many rational numbers in between two rational numbers as they are dense in nature. For instance, 2.9 is the rational number in between 2 and 3 . Example Of Rational Number For addition of these two quantities we just need to equalize the denominator first then we have to add them. We don’t need to do any application with the numerator. For equalizing the denominator we need to follow some specific rules: We have to multiply both the denominator and numerator with the same integer so the value of fraction doesn’t change and we have to multiply the integer in a manner so that the value of both the denominator will be same or for simplification you can multiply the first value by denominator of second and second value with the denominator of first. Now, let’s see how to multiply 3*5/4*5+4*4/5* 4, the denominator of first number is 4 and we have multiply it on both the numerator and denominator. Read More About Velocity and acceleration vectors of Planar curves worksheets
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The denominator of second number is 5 and we have multiplied it on both the numerator and denominator. Now, the result will be: 15/20 +16/20, Now it’s very easy we just have to add the numerator denominator remains the same so, required answer will be: 15/20 + 16/20=31/20. -2.6 is a rational number which can be written-26/10. 3.26 is a rational number which can be written 326/100. In the above mentioned examples, the first example shows the negative value and the other shows the positive value. So, second one is positive rational number. This is all about Positive Rational numbers. Some more examples of positive rational number is :4, ¼, 6 There are numbers you can possibly get when you divide one positive whole number by another one, or one negative whole number by another one. Negative Rational Numbers The numbers which are written in form of a/b where a and b are integers such that b≠0 all comes in the family of Rational Numbers. Positive Rational Numbers are those which have both numerators and denominators as positive or negative. Example: 5/7, 6/5 or (-3/-4) are positive rational numbers. Negative Rational Numbers are the numbers which have either numerator or denominator as negative. Tutorcircle.com
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Example: -3/7, -5/8 0r 5/-8 are negative rational numbers. Negative rational number must have at least one negative value that can either be numerator or denominator. Introduction to Rational numbers Today, I will tell you a story. Once there was a family of Natural numbers where all counting numbers used to live. One day a guest named zero visited the house and requested for a permission to stay there. All were happy; they requested the eldest member of the family Mr. infinite (∞) to grant the permission for 0. The permission was granted and the name of the house was changed to house of Whole numbers. Now, after some time negative numbers also visited the house and requested for the permission to be the part of the family. They were permitted and now the family became the family of Integers i.e. -∞ . ……..-3,-2,-1,0,1,2,3,…….∞. On seeing the family living together, some numbers which were in form of p/q, where p and q are natural numbers also asked for a permission to stay there. They were called fractions. Some fractions are 4/7, 2/5 …etc. The family of fractions also told that if you all see the denominator with you, which is not usually visible, then you will also become the part of fractions family. All the numbers started trying it and realized that they all are the part of fractions. But this was not true for negative integers. The meeting was held, in which it was decided that a name Rational number will be given to the family. A family of Rational Numbers consists of all the numbers which can be expressed in form of p/q, where p and q are integers, but q≠ 0.
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Published on Apr 3, 2012
The above mentioned numbers are all irrational numbers as they never terminate and repeat again and again. The numbers which are not rationa...