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Mathematics is the study of numbers and it starts from the number system. According to our level, we shall start from Real numbers. The chart below explains about the number system:
You can see a number line having a set of numbers are positive. In the figure the possesses will never end if we continue the process.So, marked numbers are called natural numbers which are denoted by N.Here, the natural numbers are 1, 2, 3, 4, 5......
Before only numbers except zero has been used. Zero usually means the emptiness which is denoted by 0. It is middle numbers between positive and negative numbers.
A set of the natural number along with zero is called whole numbers which are denoted by W. Hence, whole numbers W = 0, 1, 2, 3, . . . . . .
We know ,
Natural numbers are = 1, 2, 3, 4, 5, ....... and Negative natural numbers are = -1, -2, -3, -4, -5, ......
Therefore, the set of all positive natural numbers, negative natural numbers inclusive of zero is known as integers. It is denoted by \(\mathbb{Z}\).
So, \(\mathbb{Z}\) = ........, - 3, - 2, - 1, 0, 1, 2, 3, .......
figure
Note :
A number that can be written in the form of \(\frac{p}{q}\) where q ≠ o is called rational number .It is derived from the word ratio which also satisfies the structure \(\frac{p}{q}\}.
Note:p and q also needs to be integers
eg: \(\frac{2}{3}\) , \(\frac{5}{9}\), 0 etc .
Properties of rational numbers
Those members which can not be expressed in the form of \(\frac{a}{b} \} where a and b both are integers and b ≠ 0 , are called irrational numbers .
eg : \(\sqrt{5}\), \(\sqrt{3}\), 5\(\sqrt{7}\), \(\sqrt{3}\)+2, \(\frac{1}{2 + \sqrt{5}}\),π, 0.303003000 . . . . .
The decimals of irrational numbers are neither terminating nor repeating.
eg: In \(\sqrt{2}\) the order of \(\sqrt{2}\) is 2.
In \(\sqrt[3]{29}\) the order of \(\sqrt[3]{29}\) is 3.
Solution
\(\frac{2}{5}\)
= \(\require{enclose}\begin{array}{r}0.4\\[-3pt]5\enclose{longdiv} {20}\\[-3pt]\underline{20} \end{array}\)
Here, Divident = 2
Divisor = 5
Solution
\(\frac{1}{2}\)
= \(\require{enclose}\begin{array}{r}0.5\\[-3pt]2\enclose{longdiv} {10}\\[-3pt]\underline{10} \end{array}\)
Divident = 1
Divisor = 2
Here, \(\frac{1}{2}\)= 0.5 which is terminating decimal.
Solution
=\(\frac{1}{4}\)
=\(\require{enclose}\begin{array}{r}0.25\\[-3pt]4\enclose{longdiv}{10}\\[-3pt]\underline{8}\\[-3pt]{20}\\\underline{20}\end{array}\)
Divident = 1
Divisor= 4
Here, \(\frac{1}{4}\) = 0.25 which is terminating decimal.
Solution
\(\frac{1}{4}\)
= \(\require{enclose}\begin{array}{r}0.25\\[-3pt]4\enclose{longdiv} {10}\\[-3pt]\underline{8} \\[-3pt]20\\\underline{20}\end{array}\)
= Here, the quotient is 0.25. It is terminating after 2 decimals.
Divident= 1
Divisor = 4
The properties of rational numbers are listed below:
If the root of rational number is irrational then the resulting number is called .....................................
Determine whether the following are terminating or repeating decimals.
(frac{1}{4})
Solve the following
(frac{7}{22})
Solve the following.
(frac{2}{9})
Solve the following.
(frac{1}{2})
Rational number can also be written in ..........................................
What is this?
√5
The set of all integers is denoted by.......................
1, 2, 3, 4, 5, 6, ........ are the set of __________________________ numbers.
Solve
(frac{1}{8})
ASK ANY QUESTION ON Number System
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