# Question ec33d

Sep 27, 2015

$1 \cdot {10}^{- 8} \text{in}$

#### 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

$\text{1 in" = "2.54 cm}$

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

$\text{1 cm" = 10^7"nm}$

since you have

$\text{1 m" = 10^2"cm" implies "1 cm" = 1/10^2"m}$

and

$\text{1 cm" = 1/10^2"m" = 1/10^2 xx underbrace("1 m")_(color(blue)(=10^9"nm")) = 1/10^2 * 10^9"nm" = 10^7"nm}$

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")#