Careers360 Logo
School
Search Colleges, Exams, Schools & more
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
Upcoming Event
CBSE Class 10th  Exam Date : 17 Mar' 2025 - 17 Mar' 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.

NEET/JEE Coaching Scholarship

Get up to 90% Scholarship on Offline NEET/JEE coaching from top Institutes

Apply
Pearson | PTE

Trusted by 3,500+ universities and colleges globally | Accepted for migration visa applications to AUS, CAN, New Zealand , and the UK

Apply

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

Download PDF

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:

133125=1355

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:

178=1723

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:

64455=645×7×13

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:

151600=3×526×52151600=326×5

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:

29343=2973

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: 232352

Answer:

2323×52

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: 129227557

Answer:

12922×75×57

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:

615=2×33×5615=25

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:

3550=5×72×523550=72×5

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:

77210=7×112×3×5×777210=112×3×5

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) 133125=0.00416

(ii)&nbsnbsp; 178=2.125

(iv) 151600=0.009375

(vI) 2323×52=23200=0.115

(viii) 615=25=0.4

(ix) 3550=72×5=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=4312345678910943.123456789=4312345678929×59

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 pq 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?

43.123456789―

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.
NEET/JEE Offline Coaching
Get up to 90% Scholarship on your NEET/JEE preparation from India’s Leading Coaching Institutes like Aakash, ALLEN, Sri Chaitanya & Others.
Apply Now

Also see-

JEE Main Important Mathematics Formulas

As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

Apply

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.

Also Read

Articles

Upcoming School Exams

National Means Cum-Merit Scholarship

Application Date:17 December,2024 - 15 March,2025

Manipur Board 12th Examination

Admit Card Date:30 December,2024 - 26 March,2025

Maharashtra School Leaving Certificate Examination

Admit Card Date:20 January,2025 - 17 March,2025

Madhya Pradesh Board 12th Examination

Admit Card Date:28 January,2025 - 25 March,2025

Madhya Pradesh Board 10th Examination

Admit Card Date:29 January,2025 - 21 March,2025

View All School Exams

Certifications By Top Providers

Edx
 1115 courses
Coursera
 816 courses
Udemy
 394 courses
Futurelearn
 295 courses
Harvard University, Cambridge
 98 courses
University of Michigan, Ann Arbor
 83 courses

Explore Top Universities Across Globe

University of Essex, Colchester
  Wivenhoe Park Colchester CO4 3SQ
University College London, London
  Gower Street, London, WC1E 6BT
The University of Edinburgh, Edinburgh
  Old College, South Bridge, Edinburgh, Post Code EH8 9YL
University of Bristol, Bristol
  Beacon House, Queens Road, Bristol, BS8 1QU
University of Delaware, Newark
  Newark, DE 19716
University of Nottingham, Nottingham
  University Park, Nottingham NG7 2RD

Related E-books & Sample Papers

Questions related to CBSE Class 10th

Have a question related to CBSE Class 10th ?
i studied 1 to 10th CBSE board abroad and 11th 12th in karnataka state board . i am a domicile of karnataka and comes under minority, income under 5 lakhs. how neet councillng will allocate my seat

Hello

Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.

1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.

2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.

3. Counseling and Seat Allocation:

After the KCET exam, you will need to participate in online counseling.

You need to select your preferred colleges and courses.

Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.

4. Required Documents :

Domicile Certificate (proof that you are a resident of Karnataka).

Income Certificate (for minority category benefits).

Marksheets (11th and 12th from the Karnataka State Board).

KCET Admit Card and Scorecard.

This process will allow you to secure a seat based on your KCET performance and your category .

check link for more details

https://medicine.careers360.com/neet-college-predictor

Hope this helps you .

Read Complete Answer
Mitali Sharma 30 January,2025
show the previous year exams ?

Hello Aspirant,  Hope your doing great,  your question was incomplete and regarding  what exam your asking.

Read Complete Answer
SWETCHCHA MISKA 10 July,2024
as an icse student in class 10 is above 80 percent good enough to get into commerce in 11th cbse

Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.

Read Complete Answer
Manasvini Gupta 23 July,2024
i had cleared 10th from cbse in 2022 2 years ago now i wish to apply for 12th as private candidate in 2025. can i do so?

hello Zaid,

Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.

best of luck!

Read Complete Answer
Ashvadha 03 July,2024
i had cleared 10th in 2022 from cbse can i apply for 12th as private candidate this year?

According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.

You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.

Read Complete Answer
sadafreen356 03 July,2024
View All

Popular CBSE Class 10th Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

 Option 2)

0.16\; J
Option 3)

1.00\; J

 Option 4)

0.67\; J
Read More

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

 Option 2)

 6.45×10−3 kg
Option 3)

 9.89×10−3 kg

 Option 4)

12.89×10−3 kg

 
Read More

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

 Option 2)

200 \, \, J - 500 \, \, J
Option 3)

2\times 10^{5}J-3\times 10^{5}J

 Option 4)

20,000 \, \, J - 50,000 \, \, J
Read More

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

 Option 2)

\; K\;
Option 3)

zero\;

 Option 4)

K/4
Read More

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

 Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced
Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

 Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .
Read More

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

 Option 2)

3.125 × 10-2
Option 3)

1.25 × 10-2

 Option 4)

2.5 × 10-2
Read More

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

 Option 2)

increase two fold
Option 3)

remain unchanged

 Option 4)

be a function of the molecular mass of the substance.
Read More

With increase of temperature, which of these changes?

Option 1)

Molality

 Option 2)

Weight fraction of solute
Option 3)

Fraction of solute present in water

 Option 4)

Mole fraction.
Read More

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

 Option 2)

6.023 × 1022
Option 3)

half that in 8 g He

 Option 4)

558.5 × 6.023 × 1023
Read More

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

 Option 2)

more than 3 but less than 6
Option 3)

more than 6 but less than 9

 Option 4)

more than 9
Read More

Colleges After 12th

Applications for Admissions are open.

NEET/JEE Coaching Scholarship
NEET/JEE Coaching Scholarship
Apply

Get up to 90% Scholarship on Offline NEET/JEE coaching from top Institutes

NEET Most scoring concepts
NEET Most scoring concepts
Apply

This ebook serves as a valuable study guide for NEET 2025 exam.

NEET Previous 10 Year Questions
NEET Previous 10 Year Questions
Apply

This e-book offers NEET PYQ and serves as an indispensable NEET study material.

JEE Main Important Physics formulas
Apply

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

JEE Main Important Chemistry formulas
Apply

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

TOEFL ® Registrations 2024
Apply

Accepted by more than 11,000 universities in over 150 countries worldwide

View All Application Forms
News and Notifications
CBSE Board Exam Analysis 2025 Live: CBSE Class 10 maths paper 'easy' for most students; topics asked
March 10, 2025 - 10:17 PM IST
Rs 64.38 crore spent on Pariksha Pe Charcha while NTSE faces cuts: Education ministry data
March 10, 2025 - 04:31 PM IST
CBSE Class 10 maths paper 2025 “easy” for most, students expect above 70 marks
March 10, 2025 - 02:59 PM IST
CBSE Board Exam 2025 Live: Class 10 Hindi paper ends; difficulty level, answer key, section-wise analysis soon
February 28, 2025 - 10:29 PM IST
CBSE Class 10 Hindi Exam Analysis 2025: Paper ‘well-organised, moderately difficult'; MCQ section easy
February 28, 2025 - 02:05 PM IST
No change in CBSE Class 10 subjects for 2026, board will offer 45 languages: Chairman clarifies
February 27, 2025 - 09:35 AM IST
Minister objects to Punjabi's absence from list in CBSE draft; board says language list 'indicative'
February 26, 2025 - 12:50 PM IST

Stay up-to date with CBSE Class 10th News

Back to top