Textbook Question
The density of titanium metal is 4.506 g/cm3 at 20 °C. What is the mass of a spherical ball of titanium with a diameter of 2.00 cm. [The volume of a sphere is (4/3) πr3, where r is the radius.]
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Ch.1 - Introduction: Matter, Energy, and Measurement
Chapter 1, Problem 44
Indicate which of the following are exact numbers: (a) the mass of a 32-oz bag of sugar, (b) the number of students in your chemistry class, (c) the temperature of the surface of the Sun, (d) the mass of a postage stamp, (e) the number of milliliters in a cubic meter of water, (f) the average height of NBA basketball players.
Verified step by step guidance1
Understand that exact numbers are those that are counted or defined, not measured.
Consider (a) the mass of a 32-oz bag of sugar: This is a measured quantity, so it is not exact.
Consider (b) the number of students in your chemistry class: This is a counted quantity, so it is exact.
Consider (c) the temperature of the surface of the Sun: This is a measured quantity, so it is not exact.
Consider (e) the number of milliliters in a cubic meter of water: This is a defined quantity (1 cubic meter = 1,000,000 milliliters), so it is exact.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exact Numbers
Exact numbers are values that are counted or defined and have no uncertainty associated with them. They are typically whole numbers, such as the number of students in a class or the number of milliliters in a liter. Unlike measured quantities, exact numbers do not vary and are considered to have an infinite number of significant figures.
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Measured Numbers
Measured numbers are values obtained through measurement and inherently include some degree of uncertainty. For example, the mass of a bag of sugar or the temperature of the Sun are measured quantities, as they depend on the precision of the measuring instrument used. These numbers are subject to significant figures, which reflect the precision of the measurement.
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Significant Figures
Significant figures are the digits in a number that contribute to its precision, including all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding significant figures is crucial when performing calculations with measured numbers, as it helps convey the accuracy of the measurements and ensures that results are reported with appropriate precision.
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Related Practice
Textbook Question
For January through April 2020, at the height of the global coronavirus pandemic, it is estimated that global emissions of carbon dioxide (CO2) decreased by 940 million metric tons (1 metric ) compared to the same period in 2019. a. Express this mass of CO2 in grams without exponential notation, using an appropriate metric prefix.
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Textbook Question
Indicate which of the following are exact numbers: (a) the mass of a 3- by 5-in. index card, (b) the number of ounces in a pound, (c) the volume of a cup of Seattle's Best coffee, (d) the number of inches in a mile, (e) the number of microseconds in a week, (f) the number of pages in this book.
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Textbook Question
What is the number of significant figures in each of the following measured quantities? b. 32.40 s
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Textbook Question
What is the number of significant figures in each of the following measured quantities? d. 0.00404 L
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Textbook Question
What is the number of significant figures in each of the following measured quantities? e. 3.50×103 cm3
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