Question

Identify each of the following as measurements of length, area, volume, mass, density, time, or temperature: (a) \(25 \mathrm{ps}\), (c) \(77 \mathrm{~K},(\mathbf{d}) 100,000 \mathrm{~km}^{2},\) (b) \(374.2 \mathrm{mg}\) (e) \(1.06 \mu \mathrm{m},(\mathrm{f}) 16 \mathrm{nm}^{2}\) \((g)-78^{\circ} \mathrm{C}\) (h) \(2.56 \mathrm{~g} / \mathrm{cm}^{3}\), (i) \(28 \mathrm{~cm}^{3}\). [Section 1.4].

Short answer

(a) 25 ps: This is a measurement of time. \(ps\) stands for picoseconds, which are one trillionth (10^-12) of a second. (c) 77 K: This is a measurement of temperature. \(K\) stands for Kelvin, which is a unit for temperature in the International System of Units (SI). (d) 100,000 km^2: This is a measurement of area. \(km^2\) stands for square kilometers, which is a unit for area. (b) 374.2 mg: This is a measurement of mass. \(mg\) stands for milligrams, which are one-thousandth (10^-3) of a gram. (e) 1.06 µm: This is a measurement of length. \(µm\) stands for micrometers, which are one-millionth (10^-6) of a meter. (f) 16 nm^2: This is a measurement of area. \(nm^2\) stands for square nanometers, which is a unit for area and is equal to one-billionth (10^-18) of a square meter. (g) -78°C: This is a measurement of temperature. \(°C\) stands for degrees Celsius, which is a unit for temperature. (h) 2.56 g/cm³: This is a measurement of density. \(g/cm³\) stands for grams per cubic centimeter, which is a unit for density in the CGS system. (i) 28 cm³: This is a measurement of volume. \(cm³\) stands for cubic centimeters, which is a unit for volume in the CGS system.

Step-by-step solution

(a) 25 ps

This is a measurement of time. "ps" stands for picoseconds, which are one trillionth (10^-12) of a second.

(c) 77 K

This is a measurement of temperature. "K" stands for Kelvin, which is a unit for temperature in the International System of Units (SI).

(d) 100,000 km^2

This is a measurement of area. "km^2" stands for square kilometers, which is a unit for area.

(b) 374.2 mg

This is a measurement of mass. "mg" stands for milligrams, which are one-thousandth (10^-3) of a gram.

(e) 1.06 µm

This is a measurement of length. "µm" stands for micrometers, which are one-millionth (10^-6) of a meter.

(f) 16 nm^2

This is a measurement of area. "nm^2" stands for square nanometers, which is a unit for area and is equal to one-billionth (10^-18) of a square meter.

(g) -78°C

This is a measurement of temperature. "°C" stands for degrees Celsius, which is a unit for temperature.

(h) 2.56 g/cm³

This is a measurement of density. "g/cm³" stands for grams per cubic centimeter, which is a unit for density in the CGS system.

(i) 28 cm³

This is a measurement of volume. "cm³" stands for cubic centimeters, which is a unit for volume in the CGS system.

Key concepts

Length

Length is a fundamental way of measuring how long or short something is. It's about the distance from one end to another. We use many units to measure length depending on how big or small the object is we are measuring.

• The meter (m) is the basic SI unit used for length. It's used when talking about things like rooms, buildings, or even the height of a person.
• Kilometers (km) are used for very long distances, like when discussing travel distances between cities. One kilometer is 1,000 meters.
• For very small objects, like the thickness of hair, we use millimeters (mm) or micrometers (µm). One millimeter is one-thousandth of a meter, and one micrometer is one-millionth of a meter.

Using the right unit helps us to accurately describe and communicate measurements.

Mass

Mass measures how much matter is in an object, essentially how heavy something is. It's a key concept in considering objects' weight, though it isn't the same as weight. Mass is constant and doesn't change whether you're on Earth or the Moon.

• The basic SI unit is the kilogram (kg), useful for everyday objects like groceries or someone's weight.
• Grams (g) are used for lighter objects, with one kilogram equal to 1,000 grams.
• For very light items, such as a dose of a medicine, milligrams (mg) can be used, with 1 mg being one-thousandth of a gram.

Understanding mass helps with everything from cooking to physics.

Temperature

Temperature tells us how hot or cold something is. It's a critical measure in daily life, affecting everything from weather forecasts to cooking.

• Degrees Celsius (°C) is a common temperature scale where water freezes at 0°C and boils at 100°C.
• Kelvin (K) is another scale used mainly in science, where 0 K is absolute zero, the theoretical point where particle motion stops.

Temperature measurement keeps us prepared whether we are dressing for the day or deciding if food is done cooking.

Volume

Volume is all about how much space something occupies, whether it's a gas, liquid, or solid. It's crucial when measuring capacities, like how much water a bottle can hold or the air inside a balloon.

• The liter (L) is a common unit for volume, typically used for liquids like water or soda.
• More precise or smaller measurements might use milliliters (mL), where one liter is equal to 1,000 milliliters.
• In scientific measurements, cubic centimeters (cm³) are also common, with 1 cm³ being equivalent to 1 mL in terms of capacity.

Grasping the idea of volume helps us in tasks from measuring ingredients in recipes to understanding container sizes.