Ch.1 - Matter, Measurement & Problem Solving
Chapter 1, Problem 146
Substance A has a density of 1.7 g/cm³. Substance B has a density of 1.7 kg/m³. Without doing any calculations, determine which substance is more dense.

1
First, recognize that the units for density are different for Substance A and Substance B. Substance A is in g/cm³, while Substance B is in kg/m³.
Understand that 1 g/cm³ is equivalent to 1000 kg/m³ because 1 g = 0.001 kg and 1 cm³ = 0.000001 m³.
Convert the density of Substance A from g/cm³ to kg/m³ by multiplying by 1000. This helps to compare both densities in the same units.
Now, compare the converted density of Substance A in kg/m³ with the given density of Substance B in kg/m³.
Determine which density value is greater to identify which substance is more dense.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Density
Density is defined as mass per unit volume, typically expressed in units such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). It is a crucial property that helps in comparing the compactness of different substances. A higher density indicates that a substance has more mass in a given volume, which is essential for determining buoyancy and material properties.
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Density Concepts
Unit Conversion
Unit conversion is the process of converting a measurement from one unit to another, which is vital in comparing quantities expressed in different units. In this case, converting the density of Substance B from kg/m³ to g/cm³ is necessary to make a direct comparison with Substance A. Understanding how to convert between these units allows for accurate assessments of density.
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Conversion Factors
Comparison of Densities
When comparing densities, it is important to ensure that both substances are expressed in the same units. This allows for a straightforward determination of which substance is denser. In this scenario, recognizing that 1.7 g/cm³ is significantly greater than 1.7 kg/m³ (after conversion) is key to concluding which substance is more dense without performing calculations.
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Density Concepts
Related Practice