# How do I convert "35.0 yd" to "nm"?

Aug 24, 2016

I got $3.20 \times {10}^{10} \text{nm}$.

You can go about it in more than one way; it depends on which conversion factors you know best. I would recommend that you use the ones you definitely remember.

The general pathway I would approach it is:

$\cancel{\text{yd" xx cancel"ft"/cancel"yd" xx cancel"in"/cancel"ft" xx cancel"cm"/cancel"in" xx cancel"m"/cancel"cm" xx "nm"/cancel"m}}$

So, the conversion factors we will use are:

• $\text{3 ft}$ in one $\text{yd}$
• $\text{12 in}$ in one $\text{ft}$
• $\text{2.54 cm}$ in one $\text{in}$
• One $\text{m}$ in $\text{100 cm}$
• ${10}^{9} \text{nm}$ in one $\text{m}$

Therefore, we get:

$35.0 \cancel{\text{yd" xx (3 cancel"ft")/cancel"yd" xx (12 cancel"in")/cancel"ft" xx (2.54 cancel"cm")/cancel"in}}$
$\times \cancel{\text{m"/(100 cancel"cm") xx (10^9"nm")/cancel"m}}$

$= \textcolor{b l u e}{3.20 \times {10}^{10} \text{nm}}$

You keep three significant figures because all of these conversion factors are exact, and the measurement is known to a specific uncertainty (by default, $\pm 0.1$).

So, your answer has $3$ significant figures.