Get Real With The Real Numbers

The reality of the real numbers is introduced to in the class 10^th. Though you learn the basics of the real numbers in class 9^th, the deeper understanding becomes possible when you study the chapter in class 10^th.

The discussions of the real numbers in the ncert solutions for class 10 maths real numbers include different properties and algorithms related to the real numbers.

Here, in this article, you will find the basics of all the concepts provided in the chapter. With the initial understanding, it will get easier to enhance your knowledge during the chapter study.

So, let’s dive right into it.

1. Euclid’s Division Lemma

The Euclid’s division lemma is the algorithm that allows you to understand the properties of the positive integers. You learn about the relationship between the dividend, quotient, and remainder, which is:

·         Dividend = Divisor × Quotient + Remainder

According to Euclid’s division lemma, it is possible to get two whole numbers for the two positive integers to form a relation:

·         a = b × q + r,

·         Where 0 ≤ r < b, a and b are the positive integers, q and r are the whole numbers.

The use of this property becomes helpful in finding the highest common factor of positive integers. Also, the common properties of any two positive integers become visible easily with this property.

2. Fundamental Theorem of Arithmetic

This theorem provides properties of the composite numbers greater than 1. The theorem states that every composite number, which is greater than 1, is easily expressible as the product of two prime numbers. When it comes to the prime factorization of a number, it is easy to write the number in the powers of its prime factors.

The theorem helps in finding the highest common factors and the lowest common multiple for any two numbers. This happens due to the expression of two numbers in the form of their prime factorization.

3. Rational numbers

The identification of rational numbers becomes easier when you know how they look. The rational numbers are written as ‘x y’, where x and y are the two integers and y is not equal to 0.

You also need to know the two types of the rational numbers that occur due to the recurring or the terminating nature of the decimals.

4. Irrational numbers

Sometimes the two integers are not expressible in the form of ‘x y’ the same way possible in the rational numbers’ case. These types of numbers are called the irrational numbers.

There are various sub-properties related to the rational and irrational numbers that help in calculating the solutions.

Some important product relations between rational and irrational numbers:

·         The product of a rational and an irrational number gives an irrational number.

·         The product of two irrational numbers gives a rational or an irrational number.

Similarly, there are sum and difference related relations are available in the cbse class10 maths real numbers.

So, understand the real numbers to start your chapter with focused learning.