Compute the order of magnitude of the mass of a bathtub half full of pennies. (Assume the pennies are made entirely of copper.)

Mass = 873.6kg = 0.874 * 10^3 kg

Order = 3

Question:

Compute the order of magnitude of the mass of a bathtub half full of pennies. (Assume the pennies are made entirely of copper and the tub measures 1.3 m by 0.5 m by 0.3 m)

Explanation:

Given:

Dimensions of the tub = 1.3 m by 0.5 m by 0.3 m

Density of copper d = 8960kg/m^3

Mass = volume * density

Volume of tub = L*B*H = 1.3 * 0.5 * 0.3 = 0.195m^3

Since the tub is half full:

V = 0.195/2 = 0.0975m^3

Mass = 8960kg/m^3 * 0.0975m^3

Mass = 873.6kg = 0.874 * 10^3 kg

Order = 3

Note: Order of magnitude is of the form:

N = a * 10^b

Where;

b = order of magnitude

and

1/√10 < / = a < √10