# NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.4 Real Numbers

NCERT solutions for class 10 maths chapter 1 exercise 1.4 Real Numbers is an incredibly effective tool for students to revise the rational numbers and their decimal expansion. NCERT solutions class 10 maths chapter 1 exercise 1.4 consists of three questions, one of which is easy to solve while two are in the long answer type format.

Before proceeding to solve the exercise questions, the students are advised to remember a few of the important theorems mentioned in this segment that are given below :

- If ‘x’ is a rational number for which the decimal expansion terminates, then in that case, ‘x’ can be written in the form of p/q, ‘p’ and ‘q’ are the coprimes and the prime factorization of ‘q’ being 2
^{n}5^{m}, and ‘n’ and ‘m’ are the non-negative integers.

- If x = p/q is a rational number, where the prime factorization of ‘q’ is of the format 2
^{n}5^{m}, where ‘n’ and ‘m’ are the non-negative integers, then the decimal expansion of ‘x’ terminates.

- If a rational number, x = p/q , where ‘p’ and ‘q’ are coprimes, and the prime factorization of ‘q’ cannot be depicted as 2
^{n}5^{m}then the decimal expansion of ‘x’ can be said to be non-terminating repeating (recurring).

The students will observe that every rational number’s decimal expansion is either terminating or non-terminating, repeating.

While solving questions, the kids will also see that any real number which has a terminating decimal expansion can be expressed as a rational number, the denominator of which is a power of 10. Students can use this exercise to solve practical questions by identifying a pattern. The Class 10 Maths NCERT Solutions Chapter 1 exercise 1.4 Real Numbers are available in a scrollable PDF format below.

**☛** Download NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.4

**Exercise 1.4 Class 10 Chapter 1 **

### More Exercises in Class 10 Maths Chapter 1

- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.1
- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.2
- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.3

## NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.4 Tips

NCERT solutions class 10 maths chapter 1 exercise 1.4 Real Numbers can help students explore the decimal expansion of rational numbers. Students will come across essential terms such as terminating and non-terminating decimals. When we convert certain rational numbers into decimal form, a part of the decimal continuously repeats itself. Such decimals are called non-terminating decimals, for example, 0.333, etc. On the contrary, if no part of the decimal is repeated, the term is said to be terminating, for example, pi= 3.1415926….

NCERT solutions for class 10 maths chapter 1 exercise 1.4 is based on the above-mentioned three theorems related to the properties of rational numbers. All questions see the use of the concept of terminating and non-terminating decimals. The examples supported in this exercise can help you understand these theorems in a stepwise manner.

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## NCERT Class 10 Maths Video Solutions Chapter 1 Exercise 1.4

NCERT Videos for Class 10 Maths Chapter 1 Exercise 1.4 | |
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Question 1 | Question 3 |

Question 2 |