Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev

Class 10 : Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev

The document Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev is a part of Class 10 category.
All you need of Class 10 at this link: Class 10
NCERT Math Solutions (Exercise 1.4)
(Page 17)
Q1: 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:
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
Solution:
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
The denominator can be written in the form 5m. Hence, this decimal expansion is terminating.
 

 

Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
Since the denominator is of the form 2m so, this decimal expansion is terminating.
 
 
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
 
Since the denominator can not be written in the form 2m × 5n and it also contains other factors 7 and 13, so its decimal expansion will be non-terminating repeating type.
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
 
As the denominator is of the form 2m × 5n so, the above decimal expansion is terminating.
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
Since the denominator can not be written in the form 2m × 5n and it has 7 as its factor so, the decimal expansion of is non-terminating repeating.
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
The denominator is of the form 2m × 5n therefore, it is a terminating decimal expansion.
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
Since the denominator is not of the form 2m × 5n, and it also contain another factor 7 so, the above decimal expansion is non-terminating repeating.
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
The denominator can be written in the form 2m × 5n. Hence, the above decimal expansion is terminating.
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
Since the denominator is of the form 2m × 5n so, the above decimal expansion is a terminating one.
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
Since the denominator is not of the form 2m × 5n and also contains 3 as its factors so, the above decimal expansion is non-terminating repeating.
 
 
Q2: Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
Solution: 
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
 
 
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
 
 
 
Q3: 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 factor of q?
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
Solution:
(i) 43.123456789
This number has a terminating decimal expansion. So, it is a rational number of the form p/q and q is of the form
 
 (ii) 0.120120012000120000 …
The given decimal expansion is non-terminating and non-recurring. Therefore, it is an irrational number.
 
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics Class 10 Notes | EduRev
 
Since the given decimal expansion is non-terminating, so it is a rational number of the form p/q and q is not of the form 2m x 5n i.e., the prime factors of q will also have a factor other than 2 or 5.
 
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

ppt

,

Summary

,

shortcuts and tricks

,

Exam

,

pdf

,

Sample Paper

,

Objective type Questions

,

Mathematics Class 10 Notes | EduRev

,

Previous Year Questions with Solutions

,

past year papers

,

Math Solutions (Exercise 1.4) - Real Numbers

,

Semester Notes

,

Class 10

,

Viva Questions

,

Free

,

Extra Questions

,

practice quizzes

,

Class 10

,

Math Solutions (Exercise 1.4) - Real Numbers

,

Important questions

,

Mathematics Class 10 Notes | EduRev

,

video lectures

,

MCQs

,

Class 10

,

Math Solutions (Exercise 1.4) - Real Numbers

,

mock tests for examination

,

study material

,

Mathematics Class 10 Notes | EduRev

;