Question

Write the name of the metric unit indicated by the following symbols: (a) Tm (b) Gg (c) \(\mathrm{mL}\) (d) \(\mu\) s

Short answer

(a) Terameter, (b) Gigagram, (c) Milliliter, (d) Microsecond.

Step-by-step solution

Identifying the Unit for Tm

The symbol 'Tm' stands for 'terameter.' In the metric system, 'tera-' is a prefix that means one trillion, or \(10^{12}\). The unit 'meter' (m) is the base unit for length. Therefore, 'Tm' stands for 'terameter,' which is one trillion meters.

Identifying the Unit for Gg

The symbol 'Gg' stands for 'gigagram.' The prefix 'giga-' denotes a billion, or \(10^9\). The unit 'gram' (g) is the base unit for mass in the metric system. Thus, 'Gg' means 'gigagram,' which is one billion grams.

Identifying the Unit for mL

The symbol 'mL' represents 'milliliter.' The prefix 'milli-' denotes one thousandth, or \(10^{-3}\). The unit 'liter' (L) is a base unit for volume commonly used in the metric system. Therefore, 'mL' stands for 'milliliter,' which is one thousandth of a liter.

Identifying the Unit for \(\mu\)s

The symbol '\(\mu s\)' stands for 'microsecond.' The prefix 'micro-' is represented by the Greek letter mu (\(\mu\)) and denotes one millionth, or \(10^{-6}\). The unit 'second' (s) is the base unit for time. Thus, '\(\mu s\)' stands for 'microsecond,' which is one millionth of a second.

Key concepts

Metric System Prefixes

The metric system is widely used for measuring various quantities, such as length, mass, and volume. An essential part of this system is the use of prefixes that modify base units, making it easier to express both very large and very small numbers without using lengthy numerals.Prefixes in the metric system represent powers of ten, which allows for concise expression of measurement quantities. For example, 'kilo-' signifies a thousand, while 'mega-' indicates a million.
Some significant prefixes and their values are:

• 'nano-' (n), representing one-billionth or \(10^{-9}\)
• 'centi-' (c), representing one-hundredth or \(10^{-2}\)
• 'deci-' (d), representing one-tenth or \(10^{-1}\)
• 'milli-' (m), representing one-thousandth or \(10^{-3}\)
• 'micro-' (\(\mu\)), representing one millionth or \(10^{-6}\)
• 'giga-' (G), representing one billion or \(10^9\)
• 'tera-' (T), representing one trillion or \(10^{12}\)

These prefixes make conversions and calculations straightforward, promoting simplicity and uniformity across scientific and everyday measurements.

Base Units

The metric system is built around a set of base units. These serve as the fundamental standards for various types of measurements. Each base unit corresponds to a physical quantity. Standard base units include:

• 'meter' (m), which is the base unit for length
• 'gram' (g), which serves as the base unit for mass
• 'liter' (L), frequently used as the base unit for volume
• 'second' (s), which is the base unit for time

Using these base units, multiple measurements can be derived by simply applying the appropriate metric system prefixes. This makes it easy to work with measurements on any scale, whether you're dealing with planetary distances or microscopic phenomena.

Terameter

A 'terameter' is part of the metric measurement system and represents an incredibly vast length. The prefix 'tera-' implies a factor of one trillion, or \(10^{12}\). The terameter is thus equivalent to one trillion meters.When thinking about terameters, envision astronomical scales. These measurements are practical when discussing distances in space, such as between stars or across the Milky Way galaxy. To put it in context, a terameter can provide a frame of reference for discussing distances that are beyond our usual terrestrial encounters, adapting our understanding of space in manageable terms.

Gigagram

A 'gigagram' is utilized in the metric system when measuring substantial masses. With the prefix 'giga-' representing one billion, or \(10^9\), a gigagram equals one billion grams.Gigagrams serve essential roles in various fields such as seismology, where they help in quantifying the mass of the Earth or large geological structures. While a gigagram is rarely used in everyday situations due to its sheer magnitude, it becomes crucial when describing mass on a continental or global scale, such as the total biomass of a particular region or geological formations.

Milliliter

The 'milliliter' is a common unit with practical applications in everyday life, particularly in cooking, laboratory work, and medicine. The 'milli-' prefix represents one-thousandth, or \(10^{-3}\), meaning that a milliliter is one-thousandth of a liter.Milliliters are popular in instances where liquid volumes are measured in small quantities. Whether it's a kitchen recipe calling for a teaspoon of vanilla extract (about 5 mL) or a medical dosage, milliliters offer precision and simplicity. This small unit is convenient for various uses, promoting standard measurements to enhance clarity and accuracy in liquid handling.

Microsecond

A 'microsecond' emerges in contexts where time must be precisely measured, often at the microscopic level. With the prefix 'micro-' denoting one-millionth, or \(10^{-6}\), a microsecond is one-millionth of a second.In technology and physics, microseconds play an integral role. Applications such as signal processing, computer networks, and high-speed electronic reactions often require measurements in microseconds. This time unit helps scientists and engineers handle and interpret the minuscule intervals necessary for accurate data and responsive systems.