परिमेय संख्याएँ: Difference between revisions

Revision as of 18:46, 4 May 2024

A Number which can be represented in the form of ${\frac {p}{q}}$ where p & q are integers and q $\neq$ 0 is a Rational Number. When the rational number is divided the result will be in decimal form.

Examples:


p	q	${\frac {p}{q}}$
10	2	${\frac {10}{2}}=5$
1	1000	${\frac {1}{1000}}=0.001$
7	1	${\frac {7}{1}}=7$

Positive Rational Number

A Number which can be represented in the form of ${\frac {p}{q}}$ where q $\neq$ 0 and p & q are both positive integers is called as Positive Rational Number.

Example : ${\frac {1}{3}},{\frac {17}{3}},{\frac {3}{17}}$

Negative Rational Number

A Number which can be represented in the form of ${\frac {p}{q}}$ where q $\neq$ 0 and either p or q is a negative integer is called as Negative Rational Number.

Example : ${\frac {1}{-3}},{\frac {-17}{3}},{\frac {3}{-17}}$

Properties of a Rational Number

If we add zero to a rational number then we will get the same rational number Example : ${\frac {2}{3}}+0={\frac {2}{3}}$
A rational number remains the same if we multiply or divide both the numerator and denominator with the same factor . Example : ${\frac {2}{3}}={\frac {2X3}{3X3}}={\frac {2}{3}}$
If we add , subtract or multiply any two rational numbers the results are always a rational number. Example : ${\frac {2}{3}}+{\frac {2}{3}}={\frac {4}{3}}$

@@ Line 1: / Line 1: @@
+A Number which can be represented in the form of <math>\frac{p}{q}</math> where p & q are integers and q<math>\neq</math>0 is a Rational Number. When the rational number is divided the result will be in decimal form.
+Examples:
+{| class="wikitable"
+|+
+!p
+!q
+!<math>\frac{p}{q}</math>
+|-
+|10
+|2
+|<math>\frac{10}{2} =5</math>
+|-
+|1
+|1000
+|<math>\frac{1}{1000}=0.001</math>
+|-
+|7
+|1
+|<math>\frac{7}{1} = 7</math>
+|}
+=== Positive Rational Number ===
+A Number which can be represented in the form of <math>\frac{p}{q}</math> where q<math>\neq</math>0  and p & q are both positive integers is called as Positive Rational Number.
+Example : <math>\frac{1}{3}  , \frac{17}{3} , \frac{3}{17} </math>
+=== Negative Rational Number ===
+A Number which can be represented in the form of <math>\frac{p}{q}</math> where q<math>\neq</math>0  and either p or  q is a negative  integer is called as Negative Rational Number.
+Example : <math>\frac{1}{-3}  , \frac{-17}{3} , \frac{3}{-17} </math>
+=== Properties of a Rational Number ===
+# If we add zero to a rational number then we will get the same rational number                                                                                              Example : <math>\frac{2}{3}+0 = \frac{2}{3}</math>
+# A rational number remains the same if we multiply or divide both the numerator and denominator with the same factor .       Example : <math>\frac{2}{3} = \frac{2 X 3}{3 X 3} = \frac{2}{3}</math>
+# If we add , subtract or multiply any two rational numbers the results are always a rational number.                                        Example : <math>\frac{2}{3}+\frac{2}{3} = \frac{4}{3}</math>
 [[Category:संख्या पद्धति]]
-Rational Numbers
 [[Category:कक्षा-9]][[Category:गणित]]
 [[Category:गणित]]