CBSE Class 10th Exam Date:17 Feb' 26 - 17 Feb' 26
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.
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
Also see-
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.
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