standard notation and area

Question

A rectanglular yard has a length of 0.006 kilometer and a width of 5x10^-3 kilometer.

A) Use scientific notation to express the area of the yard in square kilomters, showing each step in the process.

B) Convert the area into square meters using the conversion below:

1 sq. kilo (km^2) = 1x10^6 sq meters (m^2)

Give your answer in standard form. Which unit is a better choice for measuring the area of the yard, and why?

Answer 1

Hi, Andrea

 

A) First step is to convert the length of the yard to scientific notation:

 

     0.006 kilometers = 6 x 10^-3 kilometers

 

     Area = length x width = (6 x 10^-3 km)*(5 x 10^-3 km) = 30 x 10^-6 km² or 3.0 x 10-5 km2

 

B)   (30 x 10^-6 km²)*(1 x 10⁶ m²/km²) =  30 m²

 

Clearly, measuring the length and width of a yard in meters is preferable to measuring those in kilometers.  30 m² is a much easier number for people to deal with than 30 x 10^-6 km² is.

 

 

Answer 2

Length is 6*10^-3 km; width is 5*10^{-3 km}; therefore, the area is 30*10^-6 sq km or 30 sq m.

 

Meters is the better choice ... easier to work with, simpler to visualize, no need for scientific notation or decimal conversion, i.e., L= 6 m, W = 5 m ... area = 6*5 = 30 square meters