When expressing an impurity of boron in silicon at 3 parts per trillion, how is this written in scientific notation?

To express 3 parts per trillion in scientific notation, it is important to understand the relationship between parts per trillion and its representation in scientific notation. One part per trillion means one part out of one trillion, or 10^12.

When you say 3 parts per trillion, you are expressing a quantity that can be represented as 3 divided by 1 trillion:

[ 3 \text{ parts per trillion} = \frac{3}{10^{12}} ]

Since 3 parts per trillion indicates that the quantity is 3 times smaller than a trillion, it corresponds directly to:

[ 3 \times 10^{-12} ]

This form clearly shows that the number 3 is multiplied by 10 raised to the negative twelfth power, which aligns perfectly with the original measurement of parts per trillion. Thus, the correct scientific notation for 3 parts per trillion is 3 x 10^-12.