Question

find 10 rational numbers between 0 and -1

Answer 1

There are an infinite number of rational numbers between 0 and 1. Some of them are: 1/2, 1/3, 1/4, 1/5, 1/6, …

That is one set of infinite numbers another with no elements in common is is 2/3, 2/5, 2/7, 2/9, … (notice I skipped 2/4 as I listed 1/2 above, and I skipped 2/6, and 2/8 etc.)

There are also an infinite number of irrational numbers between 0 and 1.

In fact, no matter how close any two distinct real numbers are, there are always an infinite number of both rational and irrational numbers between them. We say that both the rationals and the irrationals are “dense” on the real line, which means there are no little intervals that don’t contain numbers that are rational and irrational.

Answer 2

Given:

To find 10 rational numbers between 0 and -1

Solution:

Know that a number written in the form of $\[\frac{p}{q}\]$ is known as a rational number.

Write 10 rational numbers between 0 and -1,

$\[ = - \frac{1}{2}, - \frac{1}{3}, - \frac{1}{4}, - \frac{1}{5}, - \frac{1}{6}, - \frac{1}{7}, - \frac{1}{8}, - \frac{1}{9}, - \frac{1}{{10}}, - \frac{1}{{11}}\]$

Hence the required rational numbers are -

$\[ - \frac{1}{2}, - \frac{1}{3}, - \frac{1}{4}, - \frac{1}{5}, - \frac{1}{6}, - \frac{1}{7}, - \frac{1}{8}, - \frac{1}{9}, - \frac{1}{{10}}, - \frac{1}{{11}}\]$