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.

Explanation:

Step1: Set up the ratio

We want to find how many times thicker the smallest visible thing ($1\times10^{- 4}$) is compared to DNA ($3\times10^{-9}$). The formula for the ratio $R$ is $R=\frac{\text{Thickness of smallest visible thing}}{\text{Thickness of DNA}}$.

Step2: Substitute the values

Substitute the values into the formula: $R = \frac{1\times10^{-4}}{3\times10^{-9}}$.

Step3: Use the rule of exponents for division

When dividing numbers in scientific notation $a\times10^{m}\div b\times10^{n}=\frac{a}{b}\times10^{m - n}$. Here, $a = 1$, $b=3$, $m=-4$, and $n = - 9$. So, $R=\frac{1}{3}\times10^{-4-(-9)}=\frac{1}{3}\times10^{5}$.

Answer:

The thickness of the smallest thing visible to the naked eye is $\frac{1}{3}\times10^{5}$ times as thick as DNA.