# Question 57f90

Jul 10, 2017

$\left(1 \textcolor{w h i t e}{l} \text{m")/(1.0936color(white)(l)"yd}\right)$ and $\left(1 \textcolor{w h i t e}{l} \text{yd")/(0.9144color(white)(l)"m}\right)$

#### Explanation:

Let's derive them:

Wishing dimensional analysis, we can convert (1) from meters to yards and (2) from yards to meters:

1cancel("m")((100cancel("cm"))/(1cancel("m")))((1cancel("in"))/(2.54cancel("cm")))((1color(white)(l)"yd")/(36cancel("in"))) = color(red)(1.0936 color(red)("yd"#

So the first conversion factor is

$\left(1 \textcolor{w h i t e}{l} \text{m")/(1.0936color(white)(l)"yd}\right)$

Another conversion factor can be derived by taking the inverse of the number we just found:

$\frac{1}{1.0936} = 0.9144$

So we also have (the reverse conversion factor):

$\left(1 \textcolor{w h i t e}{l} \text{yd")/(0.9144color(white)(l)"m}\right)$