Arch is approx 630 ft tall How many 1/2 dollars in a stack the same height? 1 1/2 d is 2.15mm thick The GDP valued at 19,390,604,000 d. How many Arch‑height stacks of 1/2dollars to match the GDP value

Answer 1

Hi! You can work this problem out by finding some equalities and applying them using dimensional analysis. We know that 1 half-dollar is equal to 2.15 mm, so we can say 1 half-dollar = 2.15 mm. We also know that the arch is 630 ft tall. One half-dollar equals $0.50. They want us to find how many arch-height stacks of half-dollars would it take to equal $19,390,604,000.

1. First, let's find out how many half-dollars are in the height of one arch. We need to connect ft to mm, and I recommend memorizing the SI prefixes (like milli, centi, etc) and knowing some English length conversions, like ft to in and in to cm.
2. Some conversions we may want are: 1 ft = 12 in, 1 in = 2.54 cm, 100 cm = 1 m, and 1000 mm = 1 m. We also know that the arch is 630 ft, and 1 half-dollar is 2.15 mm in thickness.
3. We can now use dimensional analysis to find how many half-dollars it would take to equal one arch-height. All the units we don't want cancel out to give us a number of half-dollars.

630 ft x 12 in x 2.54 cm x 1 m x 1000 mm x 1 half-dollar = 89, 313 half-dollars

1 ft 1 in 100 cm 1 m 2.15 mm

1. Now that we know how many half-dollars can be stacked to match the height of one arch, we have a new conversion factor! 1 arch-height = 89313 half-dollars.
2. We can pull in other conversions to help us figure out how many arch-heights for the GDP. 1 arch-height = 89,313 half-dollars and 1 half-dollar = $0.50
3. If the GDP is $19,390,604,000, we can set up dimensional analysis to find the arch-heights needed for this.

$19,390,604,000 x 1 half-dollar x 1 arch-height = 434,216.83 arch-heights

$0.50 89,313 half-dollars

We likely want to round to the nearest whole number here, making the answer 434,217 arch-heights.

*Note: if you have the correct setup, but you're getting the wrong answer, try to remember to divide all the numbers on the bottoms of the fractions. Don't multiply the 89,313 in the last step, for example. This last step should be 19,390,604,000 / 0.50 / 89,313 in your calculator since anything on the bottom of the fraction is divided overall.