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.
