# What numbers are between #4.03 and 4 1/5%?

Sep 29, 2016

There are a lot of numbers between $4 \frac{1}{5}$ and $4.03$
The number midway between them (the average) would be $\textcolor{g r e e n}{4.115}$

#### Explanation:

$4 \frac{1}{5} = 4.2$

One number between the given two values is their average:
$\textcolor{w h i t e}{\text{XXX}} \frac{4.2 + 4.03}{2} = \frac{8.23}{2} = 4.115$

Sep 29, 2016

$4.03 < x < 4.2$ for $x \in \mathbb{R}$
(There are an infinity of real numbers between any two distinct points on the real line. )

#### Explanation:

$4 \frac{1}{5} = 4.2$
We are asked for a number between 4.03 and 4.2.

Let $x \in \mathbb{R}$ be the number.

Then any $x$ that satisfies: $4.03 < x < 4.2$ will meet the condition.

NB: It is interesting to note that there are infinitely many real numbers that will satisfy this condition. In fact, there are an infinity of real numbers between any two distinct points on the real line.