# Question #bc8d3

Feb 26, 2017

Approximately 4.6 Kg/m to 2 decimal ,places

Exactly $\text{ } 4 \frac{8}{13}$ Kg/m

#### Explanation:

The shortcut method is based on what follows:

I will highlight in red the bit that the shortcut method uses.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{First principle method}}$

Using ratios in fractional format.

Lookin at the units to decide how we write this. We are told
'mass per metre' so this is written as:

$\left(\text{mass")/("metres}\right) \to \frac{K g}{m} \to \frac{15}{3.25}$

The word 'per' means for each of 1. So 'per metre' is for each of 1 metre

Thus we need to change the $3.25$ metres to 1 metre
Note that $3.25 \times \frac{1}{3.25} = 1$

So we multiply top and bottom of $\frac{15}{3.25}$ by $\frac{1}{3.25}$

$\frac{\textcolor{red}{15 \times \frac{1}{3.25}}}{3.25 \times \frac{1}{3.25}} \text{ } = \frac{\textcolor{red}{15 \times \frac{1}{3.25}}}{1}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Shortcut method}}$

To determine the mass for one metre apply $\textcolor{red}{15 \div 3.25}$

Now you see where the shortcut approach comes from

This produces a decimal solution which I am choosing to be rounded, so not precise.

$15 \div 3.25 = 4.61538 \ldots . . = 4.6$ rounded to 2 decimal places

Or you can write: $\frac{15}{3.25} \times \frac{4}{4} = \frac{60}{13}$ which is an exact value