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NCERT Solutions for Exercise 1.4 Class 10 Maths Chapter 1 - Real Numbers

NCERT Solutions for Exercise 1.4 Class 10 Maths Chapter 1 - Real Numbers

Edited By Ramraj Saini | Updated on Nov 02, 2023 01:45 PM IST | #CBSE Class 10th
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CBSE Class 10th  Exam Date : 01 Jan' 2025 - 14 Feb' 2025

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

This article discuss about the class 10 maths ex 1.4 that deals with rational numbers i.e. real numbers that can be written in simple fractions p/q, where p and q are types of integers, q not equal to zero. These NCERT Solutions are created by expert team at careers360 considering the latest syllabus and pattern of the CBSE 2023-24, comprehensively covering step by step solutions of every problems.

This Story also Contains
  1. NCERT Solutions For Class 10 Maths Chapter 1 Exercise 1.4 Real Numbers
  2. Download PDF of NCERT Solutions For Class 10 Maths Chapter 1 Exercise 1.4 Real Numbers
  3. Access Exercise 1.4 Class 10 Maths Answers
  4. More About NCERT Solutions for Class 10 Maths Exercise 1.4
  5. NCERT Solutions of Class 10 Subject Wise
  6. Subject Wise NCERT Exemplar Solutions
NCERT Solutions for Exercise 1.4 Class 10 Maths Chapter 1 - Real Numbers
NCERT Solutions for Exercise 1.4 Class 10 Maths Chapter 1 - Real Numbers

In NCERT solutions for Class 10 Maths exercise 1.4 the focus is mainly on rational numbers and their decimal expansions. Most of the problems in Class 10th Maths chapter 1 exercise 1.4 are related to rational numbers that terminate or not. Along with Class 10 Maths chapter 1 exercise 1.4 the following exercises are also present.

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Download PDF of NCERT Solutions For Class 10 Maths Chapter 1 Exercise 1.4 Real Numbers

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Access Exercise 1.4 Class 10 Maths Answers

Real Numbers Class 10 Chapter 1 - Exercise 1.4

Q1 (1) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:13/3125

Answer:

\frac{13}{3125}=\frac{13}{5^{5}}

The denominator is of the form 2 a x 5 b where a = 0 and b = 5. Therefore the given rational number will have a terminating decimal expansion.

Q1 (2) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:17 / 8

Answer:

\frac{17}{8}=\frac{17}{2^{3}}

The denominator is of the form 2 a x 5 b where a = 3 and b = 0. Therefore the given rational number will have a terminating decimal expansion.

Q1 (3) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: 64 / 455

Answer:

\frac{64}{455}=\frac{64}{5\times 7\times 13}

The denominator is not of the form 2 a x 5 b . Therefore the given rational number will have a non-terminating repeating decimal expansion.

Q 1 (4) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: 15 / 1600

Answer:

\\\frac{15}{1600}=\frac{3\times 5}{2^{6}\times 5^{2}}\\ \frac{15}{1600}=\frac{3}{2^{6}\times 5}

The denominator is of the form 2 a x 5 b where a = 6 and b = 1. Therefore the given rational number will have a terminating decimal expansion.

Q 1 (5) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: 29 / 343

Answer:

\frac{29}{343}=\frac{29}{7^{3}}

The denominator is not of the form 2 a x 5 b . Therefore the given rational number will have a non-terminating repeating decimal expansion.

Q1 (6) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: \frac{23}{2 ^3 5 ^ 2 }

Answer:

\frac{23}{2 ^3 \times 5 ^ 2 }

The denominator is of the form 2 a x 5 b where a = 3 and b = 2. Therefore the given rational number will have a terminating decimal expansion.

Q1 (7) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: \frac{129 }{2 ^ 2 7^5 5 ^ 7 }

Answer:

\frac{129 }{2 ^ 2\times 7^5 \times 5 ^ 7 }

The denominator is not of the form 2 a x 5 b . Therefore the given rational number will have a non-terminating repeating decimal expansion.

Q1 (8) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: 6 / 15

Answer:

\\\frac{6}{15}=\frac{2\times 3}{3\times 5}\\ \frac{6}{15}=\frac{2}{5}

The denominator is of the form 2 a x 5 b where a = 0 and b = 1. Therefore the given rational number will have a terminating decimal expansion.

Q1 (9) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: 35 / 50

Answer:

\\\frac{35}{50}=\frac{5\times 7}{2\times 5^{2}}\\\frac{35}{50}=\frac{7}{2\times 5}

The denominator is of the form 2 a x 5 b where a = 1 and b = 1. Therefore the given rational number will have a terminating decimal expansion.

Q1 (10) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: 77 / 210

Answer:

\\\frac{77}{210}=\frac{7\times 11}{2\times 3\times5\times 7 }\\ \frac{77}{210}=\frac{11}{2\times 3\times5}

The denominator is not of the form 2 a x 5 b . Therefore the given rational number will have a non-terminating repeating decimal expansion.

Q2 Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.

Answer:

decimal expansions of rational numbers are

(i) \frac{13}{3125}=0.00416

(ii)&nbsnbsp; \frac{17}{8}=2.125

(iv) \frac{15}{1600}=0.009375

(vI) \frac{23}{2^{3}\times 5^{2}}=\frac{23}{200}=0.115

(viii) \frac{6}{15}=\frac{2}{5}=0.4

(ix) \frac{35}{50}=\frac{7}{2\times 5}=0.7

Q3 (1) The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p / q what can you say about the prime factors of q? 43.123456789

Answer:

\\43.123456789=\frac{43123456789}{10^{9}}\\ 43.123456789=\frac{43123456789}{2^{9}\times 5^{9}}

The denominator is of the form 2 a x 5 b where a = 9 and b = 9. Therefore the given number is rational and has a terminating decimal expansion.

Q3 (2) The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p / q what can you say about the prime factors of q? 0.120120012000120000

Answer:

Since the decimal part of the given number is non-terminating and non-repeating we can conclude that the given number is irrational and cannot be written in the form \frac{p}{q} where p and q are integers.

Q3 (3) The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p/q what can you say about the prime factors of q?

43. \overline{123456789}

Answer:

As the decimal part of the given number is non-terminating and repeating, the number is rational but its denominator will have factors other than 2 and 5.

More About NCERT Solutions for Class 10 Maths Exercise 1.4

Another important theorem which helps to solve problems of this class 10 ex 1.4, states that "Any rational number p/q. Be a rational number such that the prime factorisation of q is not of form 2n5m, where n, m are non-negative integers, where p and q are coprime. The rational number thus has a non-terminating repeated decimal expansion (recurring). NCERT book solutions for Class 10 Maths exercise 1.4 mainly focus on the decimal expansion of rational numbers. Questions given in the exercise 1.4 Class 10 Maths are very important for exam preparation. Students can practice 10th class maths exercise 1.4 answers to command the concepts.

Key Features of NCERT Solutions for Class 10 Maths Exercise 1.4

  • Class 10 Maths chapter 1 exercise 1.4 is thought to be the best material for problem-solving.
  • All crucial questions from exam point of view are included, and all questions from NCERT Class 10th Maths chapter 1 exercise 1.4
  • Exercise 1.4 Class 10 Maths, is founded on irrational numbers and the Fundamental Theorem of Arithmetic, both of which are key concepts in the chapter. Students can also study Real Numbers Class 10 Notes to revise the concepts quickly.

Also see-

NCERT Solutions of Class 10 Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Questions (FAQs)

1. Check whether the 17/16 have a terminating decimal or a non-terminating repeating decimal expansion.

17/16 has a terminating decimal expansion as 16 has factorisation 16=2*2*2*2, since the denominator has only 2 in the denominator.

2. Check the number is rational or irrational 44.235689.

Since the number has a terminating decimal expansion, it can be expressed in the form of p/q that is why this is a rational number.

3. Express the given rational number in p/q form, 12.1325.

Given rational number can also be written as:

12.1325=121325/10000

4. Is 0.1501500150001500001500000….. a rational number?

Since it is non-terminating and non-repeating decimal expansion, that is why it is an irrational number.

5. Discuss some properties of rational numbers.

Major properties of rational numbers are Commutative, Associative, Distributive and Closure property.

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