Lakshmi writes three rationals between 1/4 and 1/2 by repeatedly taking averages. How many rational numbers actually lie strictly between 1/4 and 1/2?

Question

Accepted Answer

infinitely many. Because rationals are dense, between any two distinct rationals there are infinitely many rationals, so there are infinitely many between 1/4 and 1/2.

Lakshmi writes three rationals between $\frac{1}{4}$ and $\frac{1}{2}$ by repeatedly taking averages.
How many rational numbers actually lie strictly between $\frac{1}{4}$ and $\frac{1}{2}$ ?

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More Class 8 Properties of Rational Numbers practice

Lakshmi writes three rationals between 41​ and 21​ by repeatedly taking averages.How many rational numbers actually lie strictly between 41​ and 21​?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Properties of Rational Numbers practice

Lakshmi writes three rationals between $\frac{1}{4}$ and $\frac{1}{2}$ by repeatedly taking averages.
How many rational numbers actually lie strictly between $\frac{1}{4}$ and $\frac{1}{2}$ ?