Question

the width of a human hair is about 1×10⁻⁴ meter wide. the width of mechanical pencil lead is about 7×10⁻⁴ meter wide. about how many pieces of hair would it take to match the width of a piece of mechanical pencil lead?

Explanation:

Step1: Set up division formula

We need to divide the width of the mechanical - pencil lead by the width of a human hair. Let $n$ be the number of hairs. Then $n=\frac{7\times 10^{-4}}{1\times 10^{-4}}$.

Step2: Use the rule of dividing numbers in scientific notation

When dividing numbers in scientific notation $\frac{a\times 10^{m}}{b\times 10^{n}}=\frac{a}{b}\times 10^{m - n}$. Here, $a = 7$, $b = 1$, $m=-4$, $n=-4$. So $n=\frac{7}{1}\times10^{-4-(-4)}=7\times10^{0}$.

Step3: Simplify the result

Since $10^{0}=1$, then $n = 7$.

Answer:

7