Question

Find a rational number between 2 1/6 and 2 1/2. write your answer as a decimal

Answer 1

To find a rational number between \(2 \frac{1}{6}\) and \(2 \frac{1}{2}\), we can first convert these mixed numbers to improper fractions or decimal form:

1. Convert \(2 \frac{1}{6}\):
\[
2 \frac{1}{6} = 2 + \frac{1}{6} = \frac{12}{6} + \frac{1}{6} = \frac{13}{6} \approx 2.1667
\]

2. Convert \(2 \frac{1}{2}\):
\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} = 2.5
\]

Now, we need to find a decimal or rational number that lies between \(2.1667\) and \(2.5\).

One possibility is to take the average of these two numbers:
\[
\text{Average} = \frac{2.1667 + 2.5}{2} = \frac{4.6667}{2} = 2.3333
\]

Thus, a rational number between \(2 \frac{1}{6}\) and \(2 \frac{1}{2}\) is \(2.3333\), which can also be expressed as:

\[
\frac{7}{3} \text{ or } 2 \frac{1}{3}
\]

So, one rational number between \(2 \frac{1}{6}\) and \(2 \frac{1}{2}\) is \(2.3333\).