Question

the diameter of a human hair is 9 · 10^(-5) meters. the diameter of a spiders silk is 3 · 10^(-6) meters. how much greater is the diameter of a human hair than the diameter of a spiders silk? write your answer in scientific notation.

Explanation:

Step1: Identify the values

The diameter of a human hair is $9\times10^{- 5}$ meters and the diameter of spider - silk is $3\times10^{-6}$ meters.

Step2: Calculate the ratio

We want to find out how many times the diameter of a human hair is greater than the diameter of spider - silk. We use the formula $\frac{\text{diameter of human hair}}{\text{diameter of spider - silk}}=\frac{9\times10^{-5}}{3\times10^{-6}}$.
Using the rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $\frac{9}{3}\times10^{-5-(-6)}$.

Step3: Simplify the expression

$\frac{9}{3}=3$ and $-5-(-6)=-5 + 6=1$. So, $\frac{9\times10^{-5}}{3\times10^{-6}}=3\times10^{1}=30$.

Answer:

$3\times10^{1}$ meters