Question

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

Short answer

By comparing the weights of 5-lb (About 5.00) bag of potatoes, 5-kg bag of sugar (About 11.02 lb), and 1-gal of water (About 8.34 lb), we can conclude that the heaviest item is the 5-kg bag of sugar, and the lightest item is the 5-lb bag of potatoes.

Step-by-step solution

Convert the weight of sugar to pounds

First, we'll convert the weight of sugar from kilograms (kg) to pounds (lb). We know that 1 kg is approximately 2.20462 lb. Therefore, the weight of sugar in pounds can be calculated as follows: Weight of sugar in pounds \( = 5 \times 2.20462 \)

Calculate the weight of 1 gallon of water in pounds

To find the weight of 1 gallon of water in pounds, we first need to convert 1 gallon to milliliters (mL) since the density is given in grams per milliliter. We know that 1 gallon is approximately 3,785.41 mL. The weight of 1 gallon of water in grams can be calculated using the given density as follows: Weight of 1 gallon of water in grams \( = 3,785.41 \times 1.0 \) Now we need to convert the weight of 1 gallon of water from grams to pounds. We know that 1 gram is approximately 0.00220462 lb. Therefore, the weight of 1 gallon of water in pounds can be calculated as follows: Weight of 1 gallon of water in pounds \( = 3,785.41 \times 0.00220462 \)

Compare the weights of the items

Now that we have the weights of all three items in pounds, we can compare them to determine which one is the heaviest and which one is the lightest. We can compare: 1. 5-lb bag of potatoes, 2. 5-kg/ [(5)(2.2046)] lb bag of sugar, and 3. 1-gal/[(3,785.41)(0.00220462)] lb of water

Determine the heaviest and the lightest item

By comparing the weights, we can conclude: 1. 5-lb (About 5.00) bag of potatoes, 2. 5-kg bag of sugar (About 11.02 lb), and 3. 1-gal of water (About 8.34 lb) Based on the comparison, the heaviest item is the 5-kg bag of sugar, and the lightest item is the 5-lb bag of potatoes.