Question

the diameter of a hydrogen atom is about 1.04x10^-10 meters. a protein molecule has an overall length of 2000 times (or 2x10^3 times) the diameter of a hydrogen atom. what is the length of the protein molecule, in meters, if it were written in scientific notation? -2.08×10^-7 meters 2.08×10^13 meters 2.08×10^-8 meters 2.08×10^-12 meters

Explanation:

Step1: Set up the multiplication

Multiply the diameter of the hydrogen atom by the factor of the protein molecule's length relative to it.
$$(1.04\times 10^{-10})\times(2\times 10^{3})$$

Step2: Multiply the coefficients and add the exponents

Using the rule \(a\times10^{m}\times b\times 10^{n}=(a\times b)\times10^{m + n}\), where \(a = 1.04\), \(b=2\), \(m=-10\), and \(n = 3\).

• Multiply the coefficients: \(1.04\times2=2.08\)
• Add the exponents: \(-10+3=-7\)

So, \((1.04\times 10^{-10})\times(2\times 10^{3})=2.08\times10^{-7}\)

Answer:

\(2.08\times 10^{-7}\) meters