what is the value of $\frac{3.0\times10^{-6}}{5.0\times10^{-3}}$ in scientific notation?\na…

what is the value of $\frac{3.0\times10^{-6}}{5.0\times10^{-3}}$ in scientific notation?\na. $0.6\times10^{-9}$\nb. $6.0\times10^{-8}$\nc. $6.0\times10^{-5}$\nd. $6.0\times10^{-4}$\ne. $0.6\times10^{-3}$

what is the value of $\frac{3.0\times10^{-6}}{5.0\times10^{-3}}$ in scientific notation?\na. $0.6\times10^{-9}$\nb. $6.0\times10^{-8}$\nc. $6.0\times10^{-5}$\nd. $6.0\times10^{-4}$\ne. $0.6\times10^{-3}$

Answer

Explanation:

Step1: Divide the coefficients

Divide 3.0 by 5.0: $\frac{3.0}{5.0}=0.6$

Step2: Divide the powers of 10

Use the rule $\frac{a^m}{a^n}=a^{m - n}$. So, $\frac{10^{-6}}{10^{-3}}=10^{-6-(-3)} = 10^{-3}$

Step3: Combine the results

The result is $0.6\times10^{-3}$. But in scientific - notation, the coefficient should be between 1 and 10. So, rewrite $0.6\times10^{-3}$ as $6.0\times10^{-4}$ (since $0.6 = 6.0\times10^{-1}$, and $0.6\times10^{-3}=(6.0\times10^{-1})\times10^{-3}=6.0\times10^{-4}$)

Answer:

D. $6.0\times 10^{-4}$