Question

How many micrometers long is one edge of a centimeter cube

Answer 1

10000 micrometers if it is one cenimeter per side

Answer 2

Answer:

10000 micrometers.

Step-by-step explanation:

We have to convert the 1cm length of the edge of the cube to micrometers Remember the following conversion units:

$1\times 10^{-6} m= 1 \mu m$ and $1\times 10^{-2} m= 1 cm$ denoting m for meters, cm for centimeters and μm or micrometers. In particular, dividing on both sides of the first equation we get the identity $1=\frac{1\mu m}{1\times 10^{-6} m}$

Combine the previous information to get:

$1 cm=1\times 10^{-2} m= (1\times 10^{-2} m) \cdot (1)= (1\times 10^{-2} m)\frac{1\mu m}{1\times 10^{-6} m}=\frac{10^{-2}}{10^{-6}}\mu m=10^4 \mu m=10000 \mu m$

Note how we "cancelled" the m symbolically as if it was a variable. This is one of the methods to convert units, and the fractions involved are known as conversion factors.