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Identify each of the following as measurements of length, area, volume, mass, density, time, or temperature: (a) \(25 \mathrm{ps}\), (b) \(374.2 \mathrm{mg}\), (c) \(77 \mathrm{~K}\), (d) \(100,000 \mathrm{~km}^{2}\), (e) \(1.06 \mu \mathrm{m}\), (f) \(16 \mathrm{nm}^{2},(\mathbf{g})-78^{\circ} \mathrm{C},(\mathbf{h}) 2.56 \mathrm{~g} / \mathrm{cm}^{3}\), (i) \(28 \mathrm{~cm}^{3}\).

Short Answer

Expert verified
(a) Time, (b) Mass, (c) Temperature, (d) Area, (e) Length, (f) Area, (g) Temperature, (h) Density, (i) Volume.

Step by step solution

01

Identify the Unit and Quantity - Part A

The unit given is \(25 \text{ ps}\). The symbol \(\text{ps}\) stands for picoseconds, which is a measurement of *time*.
02

Identify the Unit and Quantity - Part B

The unit given is \(374.2 \text{ mg}\). The symbol \(\text{mg}\) stands for milligrams, which is a measurement of *mass*.
03

Identify the Unit and Quantity - Part C

The unit given is \(77 \text{ K}\). The symbol \(\text{K}\) represents Kelvin, which is a measurement of *temperature*.
04

Identify the Unit and Quantity - Part D

The unit given is \(100,000 \text{ km}^2\). The symbol \(\text{km}^2\) stands for square kilometers, which is a measurement of *area*.
05

Identify the Unit and Quantity - Part E

The unit given is \(1.06 \mu\text{m}\). The symbol \(\mu\text{m}\) represents micrometers, which is a measurement of *length*.
06

Identify the Unit and Quantity - Part F

The unit given is \(16 \text{ nm}^2\). The symbol \(\text{nm}^2\) stands for square nanometers, which is a measurement of *area*.
07

Identify the Unit and Quantity - Part G

The unit given is \(-78^\circ \text{C}\). The symbol \(^\circ \text{C}\) stands for degrees Celsius, which is a measurement of *temperature*.
08

Identify the Unit and Quantity - Part H

The unit given is \(2.56 \text{ g/cm}^3\). The symbol \(\text{g/cm}^3\) is mass per unit volume, which identifies it as a measurement of *density*.
09

Identify the Unit and Quantity - Part I

The unit given is \(28 \text{ cm}^3\). The symbol \(\text{cm}^3\) stands for cubic centimeters, which is a measurement of *volume*.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Length
Length is a fundamental measurement of distance. It represents how long or short an object is. Length can be measured in various units, such as meters (m), centimeters (cm), millimeters (mm), kilometers (km), and even smaller scales like micrometers (µm) and nanometers (nm). Each unit serves a purpose for measuring different size scales. For instance, micrometers are often used to measure microscopic dimensions, while kilometers measure large distances, such as between cities.
It's essential to select the appropriate unit for accurate measurement based on the object's size. Whether measuring the width of a human hair or the span of a bridge, understanding length is key to many scientific and practical tasks.
Area
Area measures the space within a two-dimensional boundary, like the surface of a table or playing field. The basic unit of area is the square meter ( ext{m}^2), but there are many other units, such as square centimeters ( ext{cm}^2), square kilometers ( ext{km}^2), and smaller units like square millimeters ( ext{mm}^2).
Area calculation is crucial in various fields, from architecture to agriculture, where understanding how much space is covered or used helps in planning and design. For example, calculating the area of a wall helps determine how much paint to buy, while knowing a field's area is essential for farming.
Volume
Volume measures the amount of space an object occupies in three dimensions. It is particularly important in fields ranging from cooking and construction to chemistry and physics. Common units include cubic centimeters (cm^3), cubic meters (m^3), and liters (L). For smaller volumes, milliliters (mL) are often used.
Understanding volume is vital when determining how much liquid a container can hold or the space within a room. It also plays a role in calculating doses in medical contexts or mixing chemicals precisely in experiments.
Mass
Mass is the measurement of the amount of matter in an object, distinct from weight, which depends on gravity. Mass is constant regardless of location in the universe. The basic unit is the kilogram (kg), but there are smaller units such as grams (g) and milligrams (mg) suited for measuring smaller quantities.
Scientists often measure mass when studying properties of materials, running experiments, or creating mixed solutions. Understanding mass helps determine an object's inertia and can indirectly relate to its volume if density is known.
Density
Density is a measure of how much mass is contained in a given volume. It is often expressed in units of grams per cubic centimeter (g/cm^3) or kilograms per cubic meter (kg/m^3).
Density is a key concept in understanding buoyancy, floating, and sinking, as objects denser than the fluid they are in will sink, while those less dense will float. It's crucial in fields like material science and engineering, where understanding the density of materials can inform design decisions and quality control.
Time
Time quantifies duration and sequences of events. It's a crucial measurement in everyday life and scientific inquiry. The base unit is the second (s), and other units include minutes, hours, and smaller subdivisions like milliseconds and picoseconds (ps).
Timekeeping is essential for daily scheduling, scientific research, and understanding processes and reactions that occur in the natural world. Whether it's monitoring the duration of a chemical reaction or running a marathon, understanding time is a vital part of planning and analysis.
Temperature
Temperature measures the average kinetic energy of particles in a substance. It reflects how hot or cold something is and is a critical measurement in weather, cooking, and scientific experiments. Standard units include degrees Celsius (6C), Kelvin (K), and Fahrenheit (6F).
Temperature impacts physical properties and reactions, affecting states of matter and biological processes. Whether you're checking if food is cooked or predicting weather patterns, temperature plays an indispensable role in interpreting the world around us.

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Most popular questions from this chapter

A thief plans to steal a cylindrical platinum medal with a radius of \(2.3 \mathrm{~cm}\) and a thickness of \(0.8 \mathrm{~cm}\) from a jewellery store. If the platinum has a density of \(21.45 \mathrm{~g} / \mathrm{cm}^{3},\) what is the mass of the medal in \(\mathrm{kg}\) ?

The distance from Earth to the Moon is approximately \(240,000 \mathrm{mi} .\) (a) What is this distance in meters? (b) The peregrine falcon has been measured as traveling up to \(350 \mathrm{~km} /\) hr in a dive. If this falcon could fly to the Moon at this speed, how many seconds would it take? (c) The speed of light is \(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\). How long does it take for light to travel from Earth to the Moon and back again? (d) Earth travels around the Sun at an average speed of \(29.783 \mathrm{~km} / \mathrm{s}\). Convert this speed to miles per hour.

Indicate which of the following are exact numbers: (a) the mass of a 945-mL can of coffee, \((\mathbf{b})\) the number of students in your chemistry class, \((\mathbf{c})\) the temperature of the surface of the \(\operatorname{Sun},(\mathbf{d})\) the mass of a postage stamp, \((\mathbf{e})\) the number of milliliters in a cubic meter of water, \((\mathbf{f})\) the average height of \(\mathrm{NBA}\) basketball players.

The density of air at ordinary atmospheric pressure and \(25^{\circ} \mathrm{C}\) is \(1.19 \mathrm{~g} / \mathrm{L}\). What is the mass, in kilograms, of the air in a room that measures \(4.5 \mathrm{~m} \times 5.0 \mathrm{~m} \times 2.5 \mathrm{~m}\) ?

The total rate at which power is used by humans worldwide is approximately 15 TW (terawatts). The solar flux averaged over the sunlit half of Earth is \(680 \mathrm{~W} / \mathrm{m}^{2}\) (assuming no clouds). The area of Earth's disc as seen from the Sun is \(1.28 \times 10^{14} \mathrm{~m}^{2}\). The surface area of Earth is approximately 197,000,000 square miles. How much of Earth's surface would we need to cover with solar energy collectors to power the planet for use by all humans? Assume that the solar energy collectors can convert only \(10 \%\) of the available sunlight into useful power.

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