Question

Question #ec33d

Answer 1

`1 * 10^(-8)"in"`

Explanation:

The easiest way of doing this conversion is to go from nanometers to centimeters first, then from centimeters to inches by using the conversionf act

`"1 in" = "2.54 cm"`

So, you know that a meter is equal to `10^9` nanometers, and that a meter is also equal to `10^2` centimeters. This means that you can say that

`"1 cm" = 10^7"nm"`

since you have

`"1 m" = 10^2"cm" implies "1 cm" = 1/10^2"m"`

and

`"1 cm" = 1/10^2"m" = 1/10^2 xx underbrace("1 m")_(color(blue)(=10^9"nm")) = 1/10^2 * 10^9"nm" = 10^7"nm"`

The conversion will thus be

`0.3color(red)(cancel(color(black)("nm"))) * (1color(red)(cancel(color(black)("cm"))))/(10^7color(red)(cancel(color(black)("nm")))) * "1 in"/(2.54color(red)(cancel(color(black)("cm")))) = 1.18 * 10^(-8)"in"`

You need to round this off to one sig fig, the number of sig figs you gave for the size of the molecule

`"0.3 nm" = color(green)(1 * 10^(-8)"in")`