By using estimation techniques, determine which of the following is the heaviest and which is the lightest: a 10-lb bag of fertilizer, a 10-kg bag of rice, or 2 gal of olive oil (density = 0.918 g/cm³).

Verified step by step guidance

Convert the weight of the 10-lb bag of fertilizer to kilograms using the conversion factor 1 lb = 0.453592 kg.

The 10-kg bag of rice is already in kilograms, so no conversion is needed.

Convert the volume of 2 gallons of olive oil to liters using the conversion factor 1 gal = 3.78541 L.

Convert the volume of olive oil from liters to cubic centimeters using the conversion factor 1 L = 1000 cm³.

Calculate the mass of the olive oil using the formula mass = density × volume, where the density is given as 0.918 g/cm³, and convert the mass from grams to kilograms using the conversion factor 1 kg = 1000 g.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this question, it is essential to convert the weights of the fertilizer and rice from pounds and kilograms to a common unit, such as grams, to facilitate direct comparison. Understanding how to convert between units using conversion factors is crucial for accurate estimation.

Density

Density is defined as mass per unit volume and is a key property of substances. In this question, the density of olive oil is provided, allowing us to calculate its mass based on its volume. By applying the formula density = mass/volume, we can determine the mass of the olive oil in grams, which is necessary for comparing it with the other items.

Mass vs. Weight

Mass and weight are often confused but are distinct concepts. Mass is a measure of the amount of matter in an object, typically measured in grams or kilograms, while weight is the force exerted by gravity on that mass, measured in pounds or newtons. Understanding this difference is important when comparing the weights of the items in the question, as it influences how we interpret the values given.

Recommended video:

Guided course

1:22

Mass Percent Example

Related Practice

Textbook Question

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick. (c) How much money would this stack contain?

903

views

Textbook Question

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick.(d) The U.S. National Debt Clock showed the outstanding public debt to be $16,213,166,914,811 on October 28, 2012. How many stacks like the one described would be necessary to pay off this debt?

Textbook Question

In the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acre to a depth of exactly 1 ft. An acre is 4840 yd2. An acre-foot is enough water to supply two typical households for 1.00 yr. (a) If desalinated water costs $1950 per acre-foot, how much does desalinated water cost per liter?

755

views

Textbook Question

Two spheres of equal volume are placed on the scales as shown. a. Which one is more dense?

407

views