A rectangular yard had a length of 0.006 kilometer and a width of 5x10^-3 kilometers.
A. Use scientific notation to express the ares of the yard in kilometers, showing each step in the process.
B. Convert the area into square meters using the conversion below.
1 sq. kilometer (km^2)=1x10^6 sq. meters (m^2)
Give your answer in standard form. Which unit is a better choice formeasuring the area of the yard and why?
6*10^-3 * 5*10^-3
= 30 * 10^-6
= 3 * 10^-5 km^2
3 * 10^-5 km^2 * 10^6 m^2/km^2
= 3*10^1 = 30 m^2
30 m^2 is a lot easier to visualize than 30 millionths of a km^2
THANK YOU, thank you. I am sooo lost. I understand up to 30*10^6. I'm not sure what part is A and what part is B. Please explain in very simple terms. Thanks:-)
A. To find the area of a rectangle, we use the formula Area = Length x Width. Given the length of the yard is 0.006 kilometers and the width is 5x10^-3 kilometers, we can substitute these values into the formula.
Area = Length x Width
Area = 0.006 km x 5x10^-3 km
Step 1: Multiply the coefficients (0.006 x 5)
= 0.030
Step 2: Multiply the powers of 10 (-3 x 10^-3)
= 10^-3
Step 3: Combine the coefficient and the power of 10
= 0.030 x 10^-3
Step 4: Rewrite the coefficient as a decimal and the power of 10 as a power of 10
= 3.0 x 10^-5 km^2
Therefore, the area of the rectangular yard is 3.0 x 10^-5 km^2.
B. To convert the area from square kilometers to square meters, we use the conversion 1 sq. kilometer = 1x10^6 sq. meters.
Area in square meters = Area in square kilometers x Conversion factor
Area in square meters = 3.0 x 10^-5 km^2 x 1x10^6 m^2
Step 1: Multiply the coefficients (3.0 x 1)
= 3.0
Step 2: Multiply the powers of 10 (-5 + 6)
= 10^1
Step 3: Combine the coefficient and the power of 10
= 3.0 x 10^1 m^2
Step 4: Rewrite the coefficient and the power of 10 in standard form
= 30 m^2
Therefore, the area of the rectangular yard in square meters is 30 m^2.
For measuring the area of the yard, the unit square meters (m^2) is a better choice than square kilometers (km^2). This is because square meters are a more commonly used unit for measuring smaller areas, while square kilometers are generally used for larger areas. Using square meters makes it easier to visualize and compare the size of the yard with other familiar objects or spaces.