#### Answer

73,742 quarters

#### Work Step by Step

Because the height of a quarter is given in mm and the height of the Washington Monument is given in feet, it is necessary to convert the height of the Washington Monument into mm so that the units are the same. There are 304.8 mm in a foot.
$(\frac{375ft}{1})\times(\frac{304.8mm}{1 ft})=114300mm$
There are feet both on the top and the bottom of a fraction, so the unit feet cancel out. It is legal to multiply by $(\frac{304.8mm}{1 ft})$ because there are 304.8 mm in a foot, so it is essentially like multiplying by one, for the numbers on the top and bottom of the fraction are equal, and any number divided by itself is one.
Now, divide by the overall height by the height of a quarter in mm to get the answer.
$114300mm\div1.55mm=73,742 Quarters$
Notice, this answer is rounded to a whole number because there are no partial quarters.