NCERT Solution Class 9 Ch-1 Number System

Class 9 Chapter - 1 Number System

Numbers are the backbone of mathematics. Without numbers mathematics looks impossible. So students should have complete knowledge of number system. Before start this chapter students should go through some key points which are very important for accelerating the things.

BEFORE START NCERT CHAPTER 1 CLASS IX, STUDENTS SHOULD LEARN THE FOLLOWINGS Tables (2-20), Square tables (1-30), Cubic tables (1-20) Complete number system with definitions . Different types of decimals .

METHOD OF FINDING RATIONAL NUMBERS BETWEEN GIVEN TWO NUMBERS. Let two numbers are 2 and 3 These numbers can be written as 2.0 and 3.0 Rational numbers between 2 and 3 are as follows 2.1,  2.2,  2.3,  2.4,  2.5,  2.6,  2.7,  2.8,  2.9 etc. When two fractions are given then algorithm to find the rational numbers between two fractions Algorithm 1) Make the denominator of both the fractions equal by taking their LCM 2) Increase the gap between the numerators (if required) by multiplying by any larger number say 5, 10 etc. 3) Write the numbers between the numerators with the same denominator. Example Let two given numbers are :      and       LCM of 3 and 5 is = 15 Now make both the denominators equal to 15 \[ \frac{2}{3}\times \frac{5}{5}=\frac{10}{15}\times \frac{10}{10}=\frac{100}{150}\] \[\frac{4}{5}\times \frac{3}{3}=\frac{12}{15}\times \frac{10}{10}=\frac{120}{150}\] Rational numbers between 2/3 and 4/5 \[ \frac{101}{150},\: \frac{102}{150},\: \frac{103}{150},\: \frac{104}{150},\: \frac{105}{150},\: \frac{106}{150}\]

METHOD OF CONVERTING RATIONAL DECIMALS INTO RATIONAL NUMBER Example 1 \[ Let\: given\: number\: is=\: 2.\overline{4}\] \[Let\: x=2.\overline{4}=2.444\: \: ....\: \: (1)\] Multiplying on both side by 10 we get 10x = 10 X 2.444 10x = 24.444 .......... (2) From Eqn. (2) - eqn. (1) 9x = 22 ⇒ x = 22/9 Example 2 \[ Let\: given\: number\: is=\: 2.\overline{45}\] \[Let\: x=2.\overline{4}=2.454545\: \: ....\: \: (1)\] Multiplying on both side by 100 we get 100x = 100 X 2.4545 ........... 100x = 245.4545 .......... (2) From Eqn. (2) - eqn. (1) 99x = 243 ⇒ x = 243/99 Example 3 \[ Let\: given\: number\: is=\: 2.\overline{456}\] \[Let\: x=2.\overline{4}=2.456456\: \: ....\: \: (1)\] Multiplying on both side by 1000 we get 1000x = 1000 X 2.456456 ........... 1000x = 2456.456456 .......... (2) From Eqn. (2) - eqn. (1) 999x = 2454 ⇒ x = 2454/999

METHOD OF WRITING RATIONAL AND IRRATIONAL NUMBERS BETWEEN GIVEN TWO RATIONAL NUMBERS Algorithm 1) Write the given rational number in the decimal form upto two decimal places. 2) Write the rational numbers between the given two numbers in the decimal form. 3) Convert the given rational numbers into irrationals by placing increasing order of number of zeroes between the digits. Let given numbers are    and      =  0.7142 = 0.71 Approximately  = 0.8181... = 0.81  Approximately Irrational numbers between       and    \[ 0.72,\: \:0.73,\: \: 0.75,\: \:0.76\: \: etc \] Irrational numbers between    and   \[ 0.72072007200072\: \: .........\] \[ 0.73073007300073\: \: .........\] \[ 0.75075007500075\: \: .........\] \[ 0.76076007600076\: .......etc.\]