NCERT Grade 10, Chapter 1, Real numbers
Mathematics NCERT Grade 10, Chapter 1, Real numbers are values that are used to represent continuous quantity. The first section starts with the introduction of real numbers and the two important properties of real numbers namely:
1. Euclid's division algorithm, as the name suggests, it is related to the divisibility of integers.
It states that a positive integer 'a' can be divided by another positive integer 'b' in such a way that it leaves a remainder 'r' that is smaller than 'b'.
2. The fundamental theorem of arithmetic: It deals with the multiplication of positive integers.
- Every composite number can be expressed as a product of primes in a unique way.
This theorem has significant applications in mathematics. The two main applications of the fundamental theorem of arithmetic are cited in this section:
a. To prove the irrationality of numbers such as, 2–√, 3–√ and 5–√ .
b. To explore when exactly the decimal expansion of a rational number is terminating and when it is not terminating.
Various solved examples are given to make the problems more understandable. Section 1.4 explains the topic of revisiting irrational numbers. A number is irrational if it cannot be written in the form of p/q where q = 0. Two theorems are explained which will help in proving the irrationality of numbers. A few examples are shown that how a number is proven irrational. A short exercise is given for the assessment of students. The last section comprises of the topic- Revisiting rational numbers and their decimal expansion. Two types of decimal expansion are discussed.
- Repeating decimal expansion
- Non-repeating decimal expansion
- In this section, three theorems are included and in the last theorem it is concluded that "the decimal expansion of every rational number is either terminating or non-terminating repeating".
Video:-
Video
Link To:- Solution
Post a Comment