Class 9 NCERT Solutions - Chapter 1 Number System - Exercise 1.4

This excellent exercise is the first chapter of the Class 9 NCERT Mathematics book titled ‘’Number Systems’’, where students get acquainted with different categories of numbers rational/ irrational, and their position on the number line. Exercise 1. 4 centered on the computation and problem-solving involving decimals particularly concerning rational numbers.

Class 9 NCERT Solutions - Chapter 1 Number System - Exercise 1.4

Understanding the Decimal Representation of Rational Numbers

In Exercise 1. 4, students get to understand how to express rational numbers in terms of decimals. This section proves useful in checking when encountering a rational number if the decimal it forms is a terminating or non-terminating repeating decimal. These problems are set with a view of developing an understanding of turning a fraction into a decimal and recognizing such patterns in decimals.

Question 1. Visualize 3.765 on the number line, using successive magnification.

Solution:

Now in the given question, you have to represent 3.765 on the number line using the successive magnification method.

Step 1: We will check the range of the number and magnify it accordingly. That is, 3.765 will lie between 3 and 4 so we will magnify the value between 3 and 4.

Magnify 3 and 4

Step 2: Now 3.76 will lie between 3.7 and 3.8, so we will magnify the value between 3.7 and 3.8.

Step 3: Now as we will magnify we will check the range, that is, 3.765 will lie between 3.76 and 3.77.

Step 4: Now as we magnify the value between 3.76 and 3.77 we will find the value 3.765.

Hence 3.765 is found between 3.76 and 3.77

Question 2. Visualize 4.\overline{26}  on the number line, up to 4 decimal places.

Now in this question, we have to represent the number 4.\overline{26}  on the number line. The bar sign (   ͞   ) above .26 depicts that the number .26 is repeated continuously after the decimal point.  But it is given that we have to represent the number up to 4 decimal places only, that is, we have to represent 4.2626 on the number line.  

Step 1: We will check the range of the number and magnify it accordingly.  

Step 2: Now 4.2626 will lie between 4 and 5, so we will magnify the value between 4 and 5.

Magnify 4 and 5

Step 3: 4.26 will lie between 4.2 and 4.3, so we will magnify the value between 4.2 and 4.3.

Step 4: 4.262 will lie between 4.26 and 4.27, so we will magnify the value between 4.26 and 4.27.

Step 5: Now at last 4.2626 will lie between 4.262 and 4.263, so we will magnify the value between 4.262 and 4.263.

Step 6: As we will magnify the value between 4.262 and 4.263 we will get 4.2626.

Hence 4.2626 is found between 4.262 and 4.263

Related Articles:

• Rational and Irrational Numbers
• Class 9 RD Sharma Solutions – Chapter 1 Number System – Exercise 1.2

Summary

The purpose of Exercise 1.4 in the Class 9 NCERT Mathematics textbook is to assist students in comprehending the idea of rational numbers having decimal representations. Students gain experience working with decimal expansions and can differentiate between terminating and non-terminating repeating decimals by solving these problems.