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standard notation and area

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?

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William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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.
Alex S. | Retired, Looking to Share My Love of Mathematics and ComputersRetired, Looking to Share My Love of Mat...
4.8 4.8 (75 lesson ratings) (75)
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