Question

This is Scientific notation ( I asked the tutors on physics to help but they said go to math)

Answer 1

Remember the following property of exponentials:

`(a^n)/(a^m)=a^(n-m)`

The order of factors in a multiplication or division does not affect the result. Use this property to rearrange the factors, grouping those powers of 10 together:

`(2.5*10^3)/(4.2*10^8)=(2.5)/(4.2)*(10^3)/(10^8)`

Next, use the given property of exponentials to simpify the quotient that contains powers of 10:

`\begin{gathered} (2.5)/(4.2)*(10^3)/(10^8)=(2.5)/(4.2)*10^(3-8) \\ =(2.5)/(4.2)*10^(-5) \end{gathered}`

Calculate the quotient 2.5 / 4.2 :

`(2.5)/(4.2)*10^(-5)=0.5952\ldots*10^(-5)`

Move the decimal point one place to the right, by substracting 1 from the power of 10:

`0.5952\ldots*10^(-5)=5.952\ldots*10^(-6)`

Since the factors have 2 significant figures, round the result to 2 significant figures:

`5.952\ldots*10^(-6)\approx6.0*10^(-6)`

Therefore, the answer is:

`6.0*10^(-6)`