Question

how many meters are in 12 nanometers? express the answer in correct scientific notation. 12 nm = ? × 10^? m enter the coefficient in the green box and the exponent in the yellow box. coefficient (green) exponent (yellow)

Explanation:

Step1: Recall the conversion factor

We know that \(1\ nm = 1\times10^{-9}\ m\).

Step2: Convert 12 nm to meters

If \(1\ nm = 1\times 10^{-9}\ m\), then for \(12\ nm\), we use the formula \(12\ nm=12\times(1\times10^{-9}\ m)\).
Using the rule \(a\times(b\times c)=(a\times b)\times c\), we have \(12\times1\times10^{-9}\ m\).
Since \(12 = 1.2\times10^{1}\), then \(12\times10^{-9}\ m=(1.2\times10^{1})\times10^{-9}\ m\).
Using the rule \(a^{m}\times a^{n}=a^{m + n}\) (\(a = 10\), \(m = 1\), \(n=-9\)), we get \(1.2\times10^{1+( - 9)}\ m=1.2\times10^{-8}\ m\).

Answer:

Coefficient (green): \(1.2\)
Exponent (yellow): \(-8\)