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- Solutions 12

By using estimation techniques, determine which of the following is the heaviest and which is the lightest: a 5-lb bag of potatoes, a 5-kg bag of sugar, or 1 gal of water (density = 1.0 g/mL).

Okay guys, so in this question we have to estimate the different values and figure out is the heaviest and which one is the lightest. So we have 5 pounds of potato bags, we have 5 kilogram bag of sugar and we have 1 gallon of water that has a density of 1 gram per millilitres. So here the key is to convert all of these into the same units because then we can compare which one is the heaviest and which one is the lightest. So I am going to convert all of these 3 values into grams, so lets begin. So we have 5 pounds of potato chips and to convert to grams we know that 1 pound equals 453.6 grams. We place pounds on the bottom because we want to cancel out the units, so we have 2268 grams of potato chips not potato sorry bags of potatoes that would be a really heavy bag of potato chips. Next, we have 5-kilogram bag of sugar so to convert to grams all we do is we use our prefix, 1 goes wherever there's a prefix and kilo is 10 to the 3. We place kilogram's on the bottom to be able to cancel it out, so you have 5000 grams of sugar, bags of sugar. Finally, we have 1 gallon of water and they give us a density. So we first have to convert gallons to millilitres and then we can use the density to figure out the grams. So then we have 1 gallon of water, we know that 1 gallon equals 3.7854 litters.

We put gallons on the bottom to cancel it out. Then to convert from litters to millilitres we use our prefix, meters goes on the bottom so that we can cancel out the units. 1 goes wherever there's a prefix and milli is 10 to the negative 3 and then now we're going to use the density to change from millilitres to grams. So the density is 1 gram per 1 millilitre so we cancel out millilitres and we're left with grams. So your answer should be 3785.4 grams of water. So now lets figure out which one is the heaviest and which one is the lightest. Well we already converted everything to its mass so we just look at the highest number which in this case is going to be the bags of sugar. So the heaviest will be 5 kilogram's of sugar and the lightest is going to be the number that's the least which is the bags of potato's. So the lightest is going to be the 5 pound bags of potato's. So the key here is to convert all of the values into the same unit, when you have it into the same unit of mass then you can figure out which one is the heaviest and which one is the lightest. Alright, see you guys soon.