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What is Number System?
The number system is divided into two parts:
- Imaginary numbers
- Real numbers
Real numbers (R) are of two types:
- Rational numbers
- Irrational numbers
Rational numbers (Q)
A number that can be expressed as a/b is known as a rational number where a and b both are integers and b is not zero. Example, 5/7, -5/7, etc.
Properties of rational numbers
- The sum of rational numbers is always a rational number.
- The difference of rational numbers is always a rational number.
- The product of rational numbers is always a rational number.
- When you divide a rational number by a non-zero rational number, it gives you a rational number.
Irrational numbers (Q)
A number that cannot be expressed as a/b is known as an irrational number where a and b both are integers and b is not zero. For example, 'a' is irrational if its exact square root does not exist.
The decimal representation of rational numbers
(i) When you divide a rational number, and there is no remainder, the quotients of such divisions are called terminating decimals.
(ii) When dividing a rational number, if the division does not end, the quotients of such divisions are called non-terminating.
(iii) When a digit or a set of digits repeats continually in a non-terminating decimal, it is known as a recurring decimal.
Surds
If “y” is a positive rational integer and “a” is a positive integer, such that y1/a is irrational, y1/a is called a surd or a radical.
Rationalization
When a surd is rationalized by multiplying it with its rationalizing factor, it is known as rationalization.
- Weightage of Number System
- Illustrated examples on Number System
- FAQs on Number System
Weightage of Number System
The Number System is a basic chapter in mathematics. It is taught in Class 9 and carries eight marks.
Illustrated examples on Number System
1. Are the following statements true or false? Give reasons for your answers.
Solution.
(i). Every whole number is a natural number.
(ii) Every integer is a rational number.
(iii). Every rational number is an integer.
(i) False, because zero is a whole number but not a natural number.
(ii) True, because every integer m can be expressed in the form m/1, so it is a
rational number.
(iii) False, because ⅗ is not an integer.
2. Show that 0.3333... = 0.3 can be expressed in the form p/q, where p and
q are integers and q 0.
Solution.
Let x= 0.3333…
Now, 10x = 10 * (0.33…) = 3.333…
Now, 3.333.. = 3 + x, ( since x = 0.333…)
Thus, 10x = 3 + x
On solving, you get,
X = ⅓
3. Find an irrational number between 1/7 and 2/7.
Solution.
We know that 1/7 = 0.142857.
So we know that 2/7 = 0.285714.
A number that is non-terminating non-recurring that lies between these numbers is the required irrational number between 1/7 and 2/7.
There can be many such numbers that lie between these numbers. An example is 0.150150015000150000...
FAQs on Number System
Q: What makes real numbers?
Q: Is the negative of an irrational number also irrational?
Q: Is every irrational number a surd?
Q: Is the product of a non-zero rational number and an irrational number rational or irrational?
Q: How important is the chapter?
Maths Number System Exam
Student Forum
Anything you would want to ask experts?Answered 6 days ago
Candidates should first understand basic concepts, including divisibility rules, prime factorisation, HCF and LCM, and remainders. They should then solve topic-wise practice questions and previous years' CAT questions to improve accuracy and problem-solving speed.
S
Contributor-Level 7
Answered 6 days ago
There is no fixed number of questions from the Number System in CAT. The number of questions varies across exam slots and years. Candidates should prepare the topic along with other important areas of Quantitative Aptitude.
A
Contributor-Level 7
Answered 6 days ago
Yes, the Number System is an important topic for CAT Quantitative Aptitude. Questions may test concepts such as divisibility, remainders, factors, and properties of integers. Candidates should also practise applying these concepts to different question types.
J
Contributor-Level 7
Answered 6 days ago
The CAT Number System covers topics such as divisibility rules, factors and multiples, prime numbers, HCF and LCM, remainders, unit digits, factorials, integers, rational numbers, and properties of numbers.
Contributor-Level 10
Answered 2 months ago
CLAT does not publish a fixed count for Number System questions. The UG exam stays largely passage-based. This topic supports calculation inside Quantitative Techniques passages. It does not appear as standalone questions.
S
Contributor-Level 10
Answered 2 months ago
Number System questions cover many types. These include basic property checks, combined divisibility conditions, HCF and LCM problems, remainder patterns and multi condition reasoning. They test calculation speed and accuracy.
S
Contributor-Level 10
Answered 2 months ago
Students can improve step by step. Learn divisibility rules. Practise HCF and LCM daily. Work through remainder questions carefully. Regular revision of common traps also builds accuracy and speed.
S
Contributor-Level 10
Answered 2 months ago
There is no single fixed book for this topic. Students often use standard Class 10 level maths books. Combine these with regular practice sets and previous year papers to build accuracy.
S
Contributor-Level 10
Answered 2 months ago
Students should start early. Practice Number System alongside other Quantitative Techniques topics. Strong basics make combined divisibility and multi condition questions easier later.
S
Contributor-Level 10
Answered 2 months ago
Number System is not a separate scored CLAT topic. But the calculation skills help with passage-based Quantitative Techniques questions. Skipping it fully is not wise. Most passages need quick, accurate number work.
S
Contributor-Level 10
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