A rectangular section of wilderness will be set aside as a new wildlife refuge. Its dimensions are 5 x 10^5 meters by 4 x 10^4 meters. Find the area of the land in square meters.
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Answer: A=2*10^{10}m^2A=2∗1010m2
Step-by-step explanation:
The area of a rectangle can be calculated with this formula:
A=lwA=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)A=(5∗105m)(4∗104m)
Since 10⁵ and 10⁴ have equal base, you must add the exponents:
A=20*10^{(5+4)}m^2A=20∗10(5+4)m2
A=20*10^9m^2A=20∗109m2
Scientific notation has the form:
a*10^na∗10n
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^2A=2.0∗1010m2
Rewriting the result, you get:
A=2*10^{10}m^2A=2∗101
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