Question

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

Answer 1

I got `3.20xx10^10 "nm"`.

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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"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:

• `"3 ft"` in one `"yd"`
• `"12 in"` in one `"ft"`
• `"2.54 cm"` in one `"in"`
• One `"m"` in `"100 cm"`
• `10^9 "nm"` in one `"m"`

Therefore, we get:

`35.0 cancel"yd" xx (3 cancel"ft")/cancel"yd" xx (12 cancel"in")/cancel"ft" xx (2.54 cancel"cm")/cancel"in"`
`xx cancel"m"/(100 cancel"cm") xx (10^9"nm")/cancel"m"`

`= color(blue)(3.20xx10^10 "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.