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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.
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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Real Numbers Class 10 Chapter 1 - Exercise 1.4
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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) $\frac{35}{50}=\frac{7}{2\times 5}=0.7$
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.
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.
$43. \overline{123456789}$
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.
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
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Frequently Asked Questions (FAQs)
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.
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.
Given rational number can also be written as:
12.1325=121325/10000
Since it is non-terminating and non-repeating decimal expansion, that is why it is an irrational number.
Major properties of rational numbers are Commutative, Associative, Distributive and Closure property.
On Question asked by student community
Hello,
Yes, you can give the CBSE board exam in 2027.
If your date of birth is 25.05.2013, then in 2027 you will be around 14 years old, which is the right age for Class 10 as per CBSE rules. So, there is no problem.
Hope it helps !
Hello! If you selected “None” while creating your APAAR ID and forgot to mention CBSE as your institution, it may cause issues later when linking your academic records or applying for exams and scholarships that require school details. It’s important that your APAAR ID correctly reflects your institution to avoid verification problems. You should log in to the portal and update your profile to select CBSE as your school. If the system doesn’t allow editing, contact your school’s administration or the APAAR support team immediately so they can correct it for you.
Hello Aspirant,
Here's how you can find it:
School ID Card: Your registration number is often printed on your school ID card.
Admit Card (Hall Ticket): If you've received your board exam admit card, the registration number will be prominently displayed on it. This is the most reliable place to find it for board exams.
School Records/Office: The easiest and most reliable way is to contact your school office or your class teacher. They have access to all your official records and can provide you with your registration number.
Previous Mark Sheets/Certificates: If you have any previous official documents from your school or board (like a Class 9 report card that might have a student ID or registration number that carries over), you can check those.
Your school is the best place to get this information.
Hello,
It appears you are asking if you can fill out a form after passing your 10th grade examination in the 2024-2025 academic session.
The answer depends on what form you are referring to. Some forms might be for courses or examinations where passing 10th grade is a prerequisite or an eligibility criteria, such as applying for further education or specific entrance exams. Other forms might be related to other purposes, like applying for a job, which may also have age and educational requirements.
For example, if you are looking to apply for JEE Main 2025 (a competitive exam in India), having passed class 12 or appearing for it in 2025 are mentioned as eligibility criteria.
Let me know if you need imformation about any exam eligibility criteria.
good wishes for your future!!
Hello Aspirant,
"Real papers" for CBSE board exams are the previous year's question papers . You can find these, along with sample papers and their marking schemes , on the official CBSE Academic website (cbseacademic.nic.in).
For notes , refer to NCERT textbooks as they are the primary source for CBSE exams. Many educational websites also provide chapter-wise revision notes and study material that align with the NCERT syllabus. Focus on practicing previous papers and understanding concepts thoroughly.
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