# Question #ed60c

Mar 21, 2017

$3.5$

#### Explanation:

This new first part is in response to a query.

$\textcolor{b l u e}{\text{Additional explanation: demonstration of rounding by example}}$
I chose to use the number $23.421$ as the starting point for my example

Round to 2 decimal places

$23.42 \textcolor{red}{1} \to$round down as $\textcolor{red}{1} < 5 \to 23.42$
$23.42 \textcolor{red}{2} \to$round down as $\textcolor{red}{2} < 5 \to 23.42$
$23.42 \textcolor{red}{3} \to$round down as $\textcolor{red}{3} < 5 \to 23.42$
$23.42 \textcolor{red}{4} \to$round down as $\textcolor{red}{4} < 5 \to 23.42$

$23.42 \textcolor{red}{5} \to$round up as $\textcolor{red}{5} \ge 5 \to 23.43$
$23.42 \textcolor{red}{6} \to$round up as $\textcolor{red}{6} \ge 5 \to 23.43$
$23.42 \textcolor{red}{7} \to$round up as $\textcolor{red}{7} \ge 5 \to 23.43$
$23.42 \textcolor{red}{8} \to$round up as $\textcolor{red}{8} \ge 5 \to 23.43$
$23.42 \textcolor{red}{9} \to$round up as $\textcolor{red}{9} \ge 5 \to 23.43$

$23.43 \textcolor{red}{0} \to$round down as $\textcolor{red}{0} < 5 \to 23.43$
$23.43 \textcolor{red}{1} \to$round down as $\textcolor{red}{1} < 5 \to 23.43$
$23.43 \textcolor{red}{2} \to$round down as $\textcolor{red}{2} < 5 \to 23.43$
$23.43 \textcolor{red}{3} \to$round down as $\textcolor{red}{3} < 5 \to 23.43$
$23.43 \textcolor{red}{4} \to$round down as $\textcolor{red}{4} < 5 \to 23.43$

$23.43 \textcolor{red}{5} \to$round up as $\textcolor{red}{5} \ge 5 \to 23.44$
$23.43 \textcolor{red}{6} \to$round up as $\textcolor{red}{6} \ge 5 \to 23.44$

And so on:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$

By calculator $2 \sqrt{3} = 3.46410 \ldots .$

The dots indicate that the digits go on for a very long time.

As we need the last digit to be the ${10}^{\text{ths}}$, the cut off point is:

$\textcolor{g r e e n}{3.4 \textcolor{red}{|} 6410. \ldots}$
$\textcolor{w h i t e}{3.4} \textcolor{red}{\uparrow}$
$\textcolor{red}{\text{Cut off point}}$

We now consider the 3 units$+ \frac{4}{10} + \frac{6}{100}$

The digit to the right is 6. As this satisfies the condition of 5 or more we round up the 4 by 1 and consider all the digits to the right of the cut off point as 0's:

$\textcolor{g r e e n}{3.5000 . .} = 3.5$