Practice Density of Numbers in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The property that between any two distinct real numbers, there are infinitely many other real numbers—no two are 'adjacent'.
No matter how close two numbers are, you can always find one between them.
Example 1
mediumFind three rational numbers strictly between \dfrac{2}{5} and \dfrac{3}{5}.
Example 2
hardShow that there is an irrational number between 1 and 2, and find one explicitly.
Example 3
easyFind a rational number between 0.3 and 0.4 by averaging, and another by finding a decimal with more places.
Example 4
mediumAre there integers between 3 and 4? Are there rationals? Explain what this says about the density of integers vs. rationals.