Question

3-13 multiplying decimal fractions in practical applications example large metal parts can be electroplated in a plating bath tank. a plating bath is a solution that contains the plating metal. parts to be plated are immersed in the bath for a certain period of time. electroplating provides corrosion protection and often makes a product more attractive. an electroplater finds the number of gallons of plating bath needed for various tank sizes. find the number of gallons of plating bath needed to provide a 4 1/4 -foot bath depth in the tank shown in figure 3-11. one cubic foot of liquid contains 7.479 gallons. round the answer to the near - est ten gallons. v = l×w×h where v = volume, l = length, w = width, h = height (depth of bath) 1. compute the volume of the bath: 2. since 1 cubic foot of liquid contains 7.479 gallons.

Explanation:

Step1: Calculate bath volume

$V = l\times w\times h$, where $l = 8.20$, $w = 5.40$, $h=4\frac{1}{4}=4.25$. So $V=8.20\times5.40\times4.25$
$V = 8.20\times(5.40\times4.25)=8.20\times22.95 = 188.19$ (cubic - feet)

Step2: Convert volume to gallons

Since 1 cubic - foot contains 7.479 gallons, the number of gallons $N = V\times7.479$.
$N=188.19\times7.479$
$N = 188.19\times(7 + 0.4+0.07 + 0.009)=188.19\times7+188.19\times0.4+188.19\times0.07+188.19\times0.009$
$N = 1317.33+75.276+13.1733+1.69371$
$N = 1407.47301$

Step3: Round to the nearest ten gallons

Rounding 1407.47301 to the nearest ten gallons, we look at the ones digit. Since the ones digit is 7 (greater than 5), we round up. So $N\approx1410$ gallons.

Answer:

1410 gallons