CBSE Class 10 Exam 2023: Your Guide To Real Number Chapter

CBSE Class 10 Exam 2023: Students can look at this for revision it will help for the board examination

CBSE Class 10 Exam 2023: Your Guide To Real Number Chapter
CBSE Class 10 Exam 2023

THE CBSE class 10 board exams 2023 are expected to begin in February next year. The board is likely to release the date sheet for class 10 board exams by mid-December. As few months remain before the start of the board exams, students have started preparing for exams. This article will help students revise the Real Number chapter.

Euclid’s Division Lemma: If we have two positive integers a and b, then there exist unique integers q and r which satisfy the condition a = bq + r where 0 ≤ r < b.

The basis of the Euclidean division algorithm is Euclid’s division lemma = bq + r, 0 ≤ r < b, where q and r can also be Zero. where ‘a’ is a dividend, ‘b' is divisor, ‘q’ is quotient and ‘r’ is remainder.

∴ Dividend = (Divisor x Quotient) + Remainder

Natural Numbers: Natural numbers are part of real numbers, that include only the positive integers In this zero, decimals, fractions, and negative numbers are not included.
Example: 1, 2, 3, 4,5,6…

Whole numbers: The whole numbers are part of the number system which includes all the positive integers from 0 to infinity.
Example: 0, 1, 2, 3, 4, 5, …………….

Integers: All negative and non-negative numbers including zero altogether known as integers.
Example ………. – 3, – 2, – 1, 0, 1, 2, 3, 4, …………..

Algorithm: In an algorithm, any series of well-defined steps that shows a procedure for solving a given type of problem
Example: What is 82 divided by 3?, How many times does 3 go into 8?

Lemma: A lemma is a statement that is already proved and is used to prove other statements. It is like a mini-theorem that helps you prove a bigger theorem or statement.

Euclid’s Division Algorithm: Students use this technique to calculate the HCF (Highest common factor) of given two positive integers m and n, to calculate the HCF of two positive integers’ m and n with m > n, the following steps are followed:
First students have to apply Euclid’s division lemma to find q and r where m = nq + r, 0 ≤ r < n. Now if the remainder i.e. r = 0, then the HCF will be ‘n’ but if r ≠ 0 then we have to apply Euclid’s division lemma to n and r. Students have to continue with this process until we get the remainder as zero. Now the divisor at this stage will be HCF(m, n). Also, HCF (m, n) = HCF (n, r), where HCF (m, n) means HCF of m and n.

The Fundamental Theorem of Arithmetic: Factorise each composite number as a product of some prime numbers and of course, this prime factorisation of a natural number is unique as the order of the prime factors doesn’t matter.
LCM of given numbers is their least common multiple. If we have two positive integers ‘m’ and ‘n’ then the property of their HCF and LCM will be: HCF (m, n) × LCM (m, n) = m × n. HCF of given numbers is the highest common factor among all which is also known as greatest common divisor (GCD).

Rational Numbers: The number ‘s’ is known as a rational number if we can write it in the form of m/n where ‘m' and ‘n’ are integers and n ≠ 0, 2/3, 3/5 etc. Rational numbers can be written in decimal form also which could be either terminating or non-terminating.

Irrational Numbers: The number ‘s’ is called irrational if it cannot be written in the form of m/n, where m and n are integers and n≠0 or in the simplest form, the numbers which are not rational are called irrational numbers. Example - √2, √3 etc.

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