Question

human hair grows at a rate of about ( 6.849\times10^{-4}) cm per hour to ( 2.329\times10^{-2}) cm per hour. the rate depends on gender, genetics, age, and health. find the difference between the high end and the low end of the range. express your answer in scientific notation. do not round your answer. (1 point)

Explanation:

Step1: Make the exponents the same

We rewrite \(6.849\times 10^{-4}\) as \(0.06849\times 10^{-2}\) (since \(a\times10^{m}=b\times 10^{n}\) where \(b = a\times10^{m - n}\), here \(m=-4\), \(n = - 2\), so \(b=6.849\times10^{-4+2}=6.849\times10^{-2}\)).

Step2: Subtract the coefficients

We want to find \((2.329\times 10^{-2})-(0.06849\times 10^{-2})\). Using the distributive property \(a\times10^{n}-b\times10^{n}=(a - b)\times10^{n}\), we have \((2.329-0.06849)\times10^{-2}\).

$$2.329-0.06849=2.26051$$

Step3: Write the result in scientific notation

The result \(2.26051\times 10^{-2}\) is already in scientific notation (\(1\leqslant|a|\lt10\) and \(n\) is an integer).

Answer:

\(2.26051\times 10^{-2}\)