Question

the thickness of dna is about 3×10⁻⁹ meter. the thickness of the smallest thing visible to the naked eye is 1×10⁻⁴. compare the thickness of dna to the smallest thing visible to the naked eye. the smallest thing visible to the naked eye is 1×10⁵ times as thick as dna. the thickness of dna is 1×10⁻⁵ of the thickness of the smallest thing visible to the naked eye. the thickness of dna is 3×10⁻⁵ of the thickness of the smallest thing visible to the naked eye. the smallest thing visible to the naked eye is 1/3×10⁵ times as thick as dna.

Explanation:

Step1: Set up the ratio

To compare the thickness of DNA ($3\times10^{- 9}$) to the smallest thing visible to the naked - eye ($1\times10^{-4}$), we find the ratio $\frac{\text{Thickness of DNA}}{\text{Smallest visible thing}}=\frac{3\times10^{-9}}{1\times10^{-4}}$.

Step2: Use the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$

$\frac{3\times10^{-9}}{1\times10^{-4}}=3\times10^{-9-(-4)}=3\times10^{-9 + 4}=3\times10^{-5}$. This means the thickness of DNA is $3\times10^{-5}$ of the thickness of the smallest thing visible to the naked eye.

Answer:

The thickness of DNA is $3\times10^{-5}$ of the thickness of the smallest thing visible to the naked eye.