Question

Write the name of the metric unit indicated by the following symbols: (a) \(\mathrm{Mm}\) (b) \(\mathrm{kg}\) (c) nL (d) \(\mathrm{PS}\)

Short answer

(a) Megameter; (b) Kilogram; (c) Nanoliter; (d) Not a standard metric unit.

Step-by-step solution

Identify the Metric System Prefix

The metric system uses prefixes to denote different scales, such as kilo-, mega-, and nano-. These prefixes represent powers of ten.

Match Symbol with Prefix and Unit: Mm

The symbol 'Mm' stands for megameter. The prefix 'Mega-' denotes a factor of one million (10^6), and 'm' is the symbol for meters, which is the base unit for length in the metric system.

Match Symbol with Prefix and Unit: kg

The symbol 'kg' represents kilograms. The prefix 'kilo-' stands for a factor of one thousand (10^3), and 'g' is the symbol for grams, which is the base unit for mass in the metric system.

Match Symbol with Prefix and Unit: nL

The symbol 'nL' stands for nanoliter. The prefix 'nano-' indicates a factor of one billionth (10^{-9}), and 'L' denotes liters, which is the base unit for volume in the metric system.

Match Symbol with Prefix and Unit: PS

The symbol 'PS' does not correspond to a standard metric unit. In some contexts, 'PS' is used to denote horsepower (of German origin 'Pferdestärke'), but it is not a metric unit. For metric horsepower, the convention is typically 'kW' (kilowatts).

Key concepts

Metric System

The metric system is a universal system of measurement that is widely used around the world. Its fundamental aim is to simplify calculations within science, engineering, and everyday measurements by employing a standardized set of units.
The metric system is based on powers of ten, making it much easier to convert between units. For instance, converting meters to kilometers or grams to milligrams is just a matter of multiplying or dividing by factors of ten.

• Simplicity: Only involves a few base units for different types of measurement.
• Global standard: Used by most countries and internationally recognized in scientific research.
• Consistency: All units are interrelated and scale smoothly via steps of ten.

Understanding the metric system is crucial because it eliminates confusion in measurements and enhances precision in calculations.

Prefixes

Prefixes in the metric system denote multiples or fractions of base units. Each prefix represents a specific power of ten. This creates an easy way to express large or small quantities without writing too many zeros.
In everyday life, you might be familiar with kilometers for measuring distance or kilograms for measuring weight.

• Example 1: 'Kilo-' means a thousand, or \( 10^3 \). So, 1 kilometer (km) is 1,000 meters (m).
• Example 2: 'Mega-' signifies one million, or \( 10^6 \). Consequently, 1 megameter (Mm) is 1,000,000 meters.
• Example 3: 'Nano-' indicates a billionth, or \( 10^{-9} \). For example, 1 nanoliter (nL) equals \( 0.000000001 \) liters.

These prefixes help maintain clarity in communication about measurements and allow for straightforward conversions between units.

Powers of Ten

Understanding the concept of powers of ten is vital when dealing with metric units. Powers of ten provide a method to express numbers in a way that is both concise and easy to work with computationally.

• A positive power of ten indicates how many times to multiply the base number by ten. For example, \( 10^3 \) means 1,000.
• A negative power of ten shows how many times to divide by ten. For instance, \( 10^{-3} \) is 0.001, which represents the prefix "milli-".

This notation is the backbone of the metric system's simplicity, enabling smooth transitions between various scales. Powers of ten make it feasible to handle very large or very small measurements effortlessly.

Base Units

In the metric system, base units are the standard units from which other units are derived. They measure fundamental quantities and include units like meter (m), gram (g), and liter (L).

• Length: The meter (m) is the base unit of length. It is used globally for measuring distance or length in many contexts.
• Mass: The gram (g) serves as the base unit for mass, with kilogram (kg) being widely recognized for larger measurements.
• Volume: The liter (L) is typically the base unit for volume, especially in liquid measurements.

Using these base units, the metric system provides a common reference that allows for the precise comparison and calculation of measurements, facilitating scientific communication and practical applications worldwide.