Q1.DefinitionsEasy · 1m
Define a rational number and give one example.
Answer: A number that can be written as p/q where p and q are integers and q ≠ 0, for example 3/4.
Class 9 · Maths · Important Questions
Number System — Important Questions
Q2.Irrational NumbersMedium · 2m
Is 0.101001000100001… a rational or an irrational number? Give a reason.
Answer: Irrational — its decimal expansion is non-terminating and non-recurring.
Q3.Between NumbersMedium · 2m
Find one rational number between 1/3 and 1/2.
Answer: Take the average: (1/3 + 1/2)/2 = 5/12.
Q4.ExponentsEasy · 2m
Simplify: 2^(2/3) · 2^(1/3).
Answer: 2^(2/3 + 1/3) = 2¹ = 2.
Q5.RationalisationMedium · 3m
Rationalise the denominator of 1/(√5 − 2).
Answer: Multiply by (√5 + 2)/(√5 + 2): (√5 + 2)/((√5)² − 2²) = (√5 + 2)/(5 − 4) = √5 + 2.
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