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Chapter 1: Problem 77

By using estimation technique, determine which of the following is the heaviest and which is the lightest: a \(10-1 \mathrm{~b}\) bag of fertilizer, a \(10-\mathrm{kg}\) bag of rice, or 2 gal of olive oil (density $\left.=0.918 \mathrm{~g} / \mathrm{cm}^{3}\right)$

Short Answer

Expert verified
Based on the estimation technique, the heaviest item is the 10 kg bag of rice, weighing 10,000 g, and the lightest item is the 10-1 lb bag of fertilizer, weighing approximately 4,082.4 g.

Step by step solution

01

Convert the weights into a common unit (grams)

To compare the weights, we need to have them in a common unit. All three items have different units: pounds (lb), kilograms (kg), and gallons. We'll convert all the weights to grams (g).
02

Step 1a: Convert the bag of fertilizer weight to grams

The bag of fertilizer weighs 10-1 lb. First, we need to estimate 10 - 1 to obtain the approximate weight. 10-1 is close to 9, so we'll consider the bag of fertilizer to have an estimated weight of 9 lb. Next, we'll convert 9 lb to grams. We know that 1 lb is approximately 453.6 g. So, \( 9\ \text{lb} * 453.6\ \text{g/lb} \approx 4082.4\ \text{g} \)
03

Step 1b: Convert the bag of rice weight to grams

The bag of rice weighs 10 kg. Converting kilograms to grams, we have: \( 10\ \text{kg} * 1000\ \text{g/kg} = 10000\ \text{g} \)
04

Step 1c: Convert 2 gallons of olive oil weight to grams

First, we need to find the volume of olive oil in cubic centimeters (cm³). We know that 1 gallon is approximately 3,785.41 cm³. So, for 2 gallons, we have: \( 2\ \text{gal} * 3785.41\ \text{cm³/gal} \approx 7570.82\ \text{cm³} \) Now we can find the weight of olive oil in grams, using the given density (0.918 g/cm³). We multiply the volume by the density: \( 7570.82\ \text{cm³} * 0.918\ \text{g/cm³} \approx 6946.952\ \text{g} \)
05

Compare the weights

Now that we have the estimated weights of all three items in grams, we can compare them to determine which is the heaviest and which is the lightest. Fertilizer: \( \approx 4082.4\ \text{g} \) Rice: \( = 10000\ \text{g} \) Olive oil: \( \approx 6946.952\ \text{g} \) Comparing the estimated weights, we can conclude that the heaviest is the bag of rice (10,000 g), and the lightest is the bag of fertilizer (approx. 4,082.4 g).

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Most popular questions from this chapter

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