Conversions!
posted by Lena on .
1. The price of gold is 200 dollars/oz. How much did 1 g of gold cost that day? (1 oz = 28.4 g)Use dimensional analysis.
2. How many minutes does it take light from the sun to reach Earth? (Distance from sun to Earth is 93 million mi, speed of light= 3 x 10^8 m/s) Use dimensional analysis.
Please, and thank you!

These are easy to do if you follow through and check the units. All of them are as follows:
something x factor = another unit.
For #1.
We have gold at 200 dollars per oz. We want to convert that to dollars per gram. The problem tells us that the factor is 1 oz = 28.4 and we can write that as 1 oz/28.4 g OR 28.4 g/1 oz.
cost per gram = cost per oz x factor
cost per g = $200/oz x (1 oz/28.4 g) =??.
Note that oz in the denominator of the first term will cancel with the oz in the numerator of the second term and we are left with $/g for the cost which is what we want. We COULD have written $200/oz x (28.4 g/1 oz) but then the final answer would be in units of $*g/oz^{2} and that is NOT the unit we want. You will ALWAYS know which way to place the factor if you follow the units and make sure the final unit is the one you want. I hope this helps. I will leave #2 for you for practice. 
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