Question

Choose the option with the proper number of sig figs

Answer 1

Step 1: Write out the given standard form

$\frac{7\times10^{-8}}{(3\times10^4)(5\times10^5)}$

Step 2: To determine the scientific notification of the given standard form

To achieve this, we would apply the rule of indices

The addition rule of indices is given as:

$(a\times m^x)(b\times m^y)=(a\times b)m^{x+y}$

Apply the rule to solve the given expression as shown below:

$\begin{gathered} (3\times10^4)(5\times10^5) \\ =(3\times5)\times10^{4+5} \\ =15\times10^9 \end{gathered}$

So,

$\frac{7\times10^{-8}}{(3\times10^4)(5\times10^5)}=\frac{7\times10^{-8}}{15\times10^9}$

The subtraction rule of indices is

$\frac{m^x}{m^y}=m^{x-y}$

Applying the subtraction rule of indices would give us

$\begin{gathered} \frac{7\times10^{-8}}{15\times10^9}=\frac{7}{15}\times10^{-8-9} \\ \frac{7}{15}\times10^{-8-9}=0.47\times10^{-17} \end{gathered}$

Hence, the scientific notification of the given expression is 0.47 x 10⁻¹⁷