alleryHow many rational numbers are there between any two distinct rationals?
AExactly one
BExactly ten
CInfinitely many
DDepends on the two rationals
Answer & Solution
Correct answer: C. Infinitely many
This is the density property of rational numbers.
Between any two distinct rationals a and b, there are infinitely many other rationals.
**One way to construct:** keep taking averages (a+b)/2
then average each new value with one of a, b
and so on — every step gives a new rational.
This is why rationals 'fill' the number line densely (though irrationals fill the remaining gaps).
Keep practising Unit 1B2: Algebraic Limits and Continuity
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