Question

345nm=____mm
I need to see how to work the problem out​

Answer 1

3.45×10⁻⁴mm (or 0.000345mm)

Step-by-step explanation:

Use a method called dimensional analysis here. It involves a chain of conversions, so we'll need some conversions to work with.

• 1nm = 1×10⁻⁹m
• 1mm = 1×10⁻³m
• 345nm; which is given

If you knew the conversion from nanometers to millimeters then you could just do it in one step. But I don't, so I won't. Anyways, you put the conversions into fraction form like so:

• 1nm/1×10⁻⁹m
• 1mm/1×10⁻³m

And then orient them in a way where multiplying the two (or more in other instances) gives you the units you want. In this cas it's millimeters so you'll have:

(345nm)•(1×10⁻⁹m/1nm)•(1mm/1×10⁻³m)

Notice how all the units reduce except for mm. From here you just multiply across and should get 345×10⁻⁶mm which simplifies to 3.45×10⁻⁴mm.