Rational numbers, Mathematics

Assignment Help:

Although the set of integers caters to a larger audience, it is inadequate. This inadequacy has led to the formulation of Rational numbers. Rational numbers are of the form p/q, where p and q are integers and q  ≠ 0. The numbers like  2/3,-5/4 are examples of rational numbers. The set of rational numbers are denoted by Q and generally expressed as:

Q = {........, 210_rational numbers.png , ......}

In the set of rational numbers if you consider any of the element say -2/5, we observe that the quotient is - 0.4. Similarly if you consider 7/8, the quotient is 0.875. In both these cases the decimal part is terminating. By terminating, we understand that the division process is coming to an end. Now, in the same set, consider the element 6/7. For this number the quotient is 0.857142857142...... In this case we observe that the decimal part is (i) not terminating and (ii) repeating.

But on occasions we find decimals which neither terminate nor repeat. For instance, consider a number like 65/67. The quotient is of the form 0.970149253..... In this quotient we neither find the decimal terminating nor repeating. Numbers whose decimals are non-terminating and non-repeating are included in a set of numbers called irrational numbers.               


Related Discussions:- Rational numbers

Sequences and series - calculus, Sequences and Series In this section ...

Sequences and Series In this section we will be taking a look at sequences and infinite series.  In fact, this section will deal approximately exclusively with series.  Though

Two train leave show many hours will take before trains pass, Two trains le...

Two trains leave two different cities 1,029 miles apart and head directly toward every other on parallel tracks. If one train is traveling at 45 miles per hour and the other at 53

Ratio, There are only Chinese and Malay pupils in a hall.The ratio of the n...

There are only Chinese and Malay pupils in a hall.The ratio of the number of boys to the number of girls is 2:3.The ratio of the number of Chinese boys to the number of Malay boys

Quadriatic-equations, Q. a(b - c)x^2 + b(c - a)x + c(a - b) = 0 has equal r...

Q. a(b - c)x^2 + b(c - a)x + c(a - b) = 0 has equal roots then b = ? Ans: Condition that a quadratic equation ax² + bx + c = 0 has equal roots is: Its discriminant, b² - 4ac = 0 A

Domain and range of a function , Domain and range of a functio:  One of th...

Domain and range of a functio:  One of the more significant ideas regarding functions is that of the domain and range of a function. In simplest world the domain of function is th

Evaluate integrals, Evaluate following integrals.  (a) ∫ 3e x + 5 cos x...

Evaluate following integrals.  (a) ∫ 3e x + 5 cos x -10 sec 2   x dx  (b) ( 23/ (y 2 + 1) + 6 csc y cot y + 9/ y dy Solution (a)    ∫ 3e x + 5 cos x -10 sec 2 x

Normal to y=f(x) , If the normal to y=f(x) makes an angle of pie/4 with y-a...

If the normal to y=f(x) makes an angle of pie/4 with y-axis at (1,1) , then f''(x) is eqivalent to? Ans) The normal makes an angle 135 degree with the x axis. also f ''(1)

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd