Question

A rectangular section of wilderness will be set aside as a new wildlife refuge. Its dimensions are 5 x 105meters by 4 x104 meters. Find the area of the land in square meters. Make sure your answer is in correct scientific notation form

Answer 1

Answer: $A=2*10^{10}m^2$

Step-by-step explanation:

The area of a rectangle can be calculated with this formula:

$A=lw$

Where "l" is the lenght and "w" is the width.

You know that the dimensions of this rectangle are 5*10⁵meters and 4*10⁴ meters, then you need to multiply them to get the area:

$A=(5*10^5m)(4*10^4m)$

Since 10⁵ and 10⁴ have equal base, you must add the exponents:

$A=20*10^{(5+4)}m^2$

$A=20*10^9m^2$

Scientific notation has the form:

$a*10^n$

Where "a" is any number between 1 and 10 but less than 10, and "n" is an integer.

Since 20 is greater than 10, you must move the decimal point to the left:

$A=2.0*10^{10}m^2$

Rewriting the result, you get:

$A=2*10^{10}m^2$