Question

Choose the option with the proper number of sig figs

Answer 1

Step 1: Write out the given standard form

`(7*10^(-8))/((3*10^4)(5*10^5))`

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* m^x)(b* m^y)=(a* b)m^(x+y)`

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

`\begin{gathered} (3*10^4)(5*10^5) \\ =(3*5)*10^(4+5) \\ =15*10^9 \end{gathered}`

So,

`(7*10^(-8))/((3*10^4)(5*10^5))=(7*10^(-8))/(15*10^9)`

The subtraction rule of indices is

`(m^x)/(m^y)=m^(x-y)`

Applying the subtraction rule of indices would give us

`\begin{gathered} (7*10^(-8))/(15*10^9)=(7)/(15)*10^(-8-9) \\ (7)/(15)*10^(-8-9)=0.47*10^(-17) \end{gathered}`

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