3. What is a Rational Number?
A rational number, in Mathematics, can be defined
as any number which can be represented in the
form of p/q where q ≠ 0.
4. Conversion of a Mixed Recurring Decimal in the Form of p/q:-
• Examples:-
• Express the following decimal in the form of p/q:-
• A) 0.32222......{BAR ON 2}
• Sol:-Let x be = 0.322222......(Eq-1)
∴ Multiplying Both sides by 10.
• 10x = 3.2222.......(Eq-2)
• Subtracting (Eq-2) - (Eq-1)
• 10x – x = 3.2222.... - 0.32222.....
• 9x = 2.9
• X = 2.9/9
• X= 29/90 { By removing the decimal }
5. • Examples:-
• Express the following decimal in the form of p/q:-
• B) 0.12333......{BAR ON 3}
• Sol:-Let x be 0.123333......(Eq-1)
• ∴ Multiplying Both sides by 10.
• 10x = 1.2333.......(Eq-2)
• Subtracting (Eq-2) - (Eq-1)
• 10x – x = .... - 1.2333..... - 0.12333......
• 9x = 1.11
• X = 1.11/9
• X= 111/900 { By removing the decimal }
6. • Examples:-
• Express the following decimal in the form of p/q:-
• C) 0.111.....{BAR ON 1}
• Sol:-Let x be = 0.11111.....(Eq-1)
• ∴ Multiplying Both sides by 10.
• 10x = 1.1111.......(Eq-2)
• Subtracting (Eq-2) - (Eq-1)
• 10x – x = 1.1111... - 0.11111.....
• 9x = 1
• X = 1/9
7. • Examples:-
• Express the following decimal in the form of p/q:-
• D) 0.6666......{BAR ON 6}
• Sol:-Let x be = 0.666666.....(Eq-1)
• ∴ Multiplying Both sides by 10.
• 10x = 6.66666.......(Eq-2)
• Subtracting (Eq-2) - (Eq-1)
• 10x – x = 6.66666... - 0.66666.....
• 9x = 6
• X = 2/3
8. • Examples:-
• Express the following decimal in the form of p/q:-
• E) 0.001 {BAR ON 001}
• Sol:-Let X be = 0.001.....(Eq-1)
• ∴ Multiplying Both sides by1000.
• 1000x = 001.001001001.......(Eq-2)
• Subtracting (Eq-2) - (Eq-1)
• 1000x – x = 001.001001.... - 0.001001001.....
• 999x = 1
• X = 1/999
