Question

human skin has a thickness of about 5×10⁻³ meter. a grain of sand has a thickness of about 1×10⁻³ meter. about how many grains of sand would it take to match the thickness of human skin? grains of sand (1×10⁻³) human skin (5×10⁻³)

Explanation:

Step1: Set up division formula

To find the number of sand - grains, divide skin thickness by sand - grain thickness. Let $n$ be the number of sand - grains. Then $n=\frac{5\times10^{-3}}{1\times10^{-3}}$.

Step2: Use exponent rule for division

When dividing numbers in scientific notation with the same base ($10$ in this case), we subtract the exponents. $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. Here, $a = 5$, $b = 1$, $m=-3$, $n=-3$. So $n=\frac{5}{1}\times10^{-3-(-3)}=5\times10^{0}$.

Step3: Simplify the result

Since any non - zero number to the power of $0$ is $1$ ($10^{0}=1$), then $n = 5\times1=5$.

Answer:

5