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NCERT Solution Class 9 Ch1 Number System
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BEFORE START NCERT CHAPTER 1 CLASS IX, STUDENTS SHOULD LEARN
THE FOLLOWINGS

METHOD OF FINDING RATIONAL NUMBERS BETWEEN GIVEN TWO NUMBERS. Let
two numbers are 2 and 3
LCM of 3 and 5 is = 15 
METHOD OF CONVERTING RATIONAL DECIMALS INTO RATIONAL NUMBER Example 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 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 Irrational numbers between and \[ 0.72,\: \:0.73,\: \: 0.75,\: \:0.76\: \: etc \] Irrational numbers between and 
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