Question

Write the numbers represented by the following prefixes: (a) mega-, (b) kilo-, (c) deci-, (d) centi-, (e) milli-, (f) micro-, \((\mathrm{g})\) nano-, \((\mathrm{h})\) pico-

Short answer

Mega- is 10^6; kilo- is 10^3; deci- is 10^{-1}; centi- is 10^{-2}; milli- is 10^{-3}; micro- is 10^{-6}; nano- is 10^{-9}; pico- is 10^{-12}.

Step-by-step solution

Understanding Metric Prefixes

Metric prefixes represent different powers of ten, making it easier to express large or small quantities. Each prefix has a specific numerical value associated with it.

Mega-

The prefix 'mega-' represents a factor of \(10^6\). Thus, mega- corresponds to 1,000,000.

Kilo-

The prefix 'kilo-' represents a factor of \(10^3\). Therefore, kilo- corresponds to 1,000.

Deci-

The prefix 'deci-' represents a factor of \(10^{-1}\). This means deci- corresponds to 0.1.

Centi-

The prefix 'centi-' represents a factor of \(10^{-2}\). Centi- corresponds to 0.01.

Milli-

The prefix 'milli-' represents a factor of \(10^{-3}\). Hence, milli- corresponds to 0.001.

Micro-

The prefix 'micro-' represents a factor of \(10^{-6}\). Micro- corresponds to 0.000001.

Nano-

The prefix 'nano-' represents a factor of \(10^{-9}\). Thus, nano- corresponds to 0.000000001.

Pico-

The prefix 'pico-' represents a factor of \(10^{-12}\). Pico- corresponds to 0.000000000001.

Key concepts

Powers of Ten

In mathematics and science, the concept of powers of ten is a vital tool that simplifies the representation of both large and small numbers. When we speak of powers of ten, we refer to numbers that can be expressed as 10 raised to an exponent. This exponential notation makes it easier to work with extremely large or tiny values.
The exponent in a power of ten notes how many times 10 is multiplied by itself. For instance:

• \(10^1 = 10\)
• \(10^2 = 100\)
• \(10^3 = 1,000\)

The further you progress up the scale, the larger the numbers become. Conversely, negative exponents, like \(10^{-1}, 10^{-2}\), represent fractions, which are useful for denoting very small quantities such as millimeters or micrometers. Understanding this notation allows us to use metric prefixes efficiently, making it easier to communicate scientific measurements with precision.

Mega

The prefix 'mega-' is part of the metric system, commonly used to denote one million times a unit. It is consistently represented by the power of ten notation \(10^6\). In numerical terms, mega- equals 1,000,000.
Mega is often used in various scientific fields, engineering, and everyday applications, for instance, to express units of measurement such as:

• Megahertz (MHz), which means a million hertz or cycles per second.
• Megabytes (MB), measuring millions of bytes in digital storage.
• Megawatts (MW), referring to one million watts of power.

Remember that when you see 'mega-', it's a straightforward conversion to the number one million, easing the understanding and communication of large quantities.

Kilo

The 'kilo-' prefix is another fundamental component of the metric system, symbolizing a thousandfold increment, or \(10^3\). Thus, kilo- translates to 1,000.
It’s frequently encountered in various contexts and is one of the most familiar prefixes for everyday use. Consider the following examples:

• Kilogram (kg), commonly used for measuring weight, equaling 1,000 grams.
• Kilometer (km), a standard unit for measuring distance, equivalent to 1,000 meters.
• Kilowatt (kW), a measure of electrical power equaling 1,000 watts.

When understanding everyday measurements, the kilo- prefix allows us to simplify numbers and communicate the scale of measurement with ease. Knowing that kilo- means 1,000 can help you quickly interpret these units without any complexity.

Micro

The prefix 'micro-' denotes a very small scale, specifically one millionth of a unit. It is expressed as \(10^{-6}\), indicating the decimal 0.000001.
Due to its utilization in representing tiny measurements, micro- is commonly found in various scientific and technological fields. Some examples where 'micro-' is applied include:

• Micrometer (also known as a micron), which is 0.000001 meter or one-millionth of a meter, useful in measuring small object dimensions.
• Microgram (µg), representing a mass of one-millionth of a gram, used in medical and nutritional fields.
• Microsecond (µs), which divides a second into one million parts, applicable in fields like physics and electronics.

Utilizing the micro- prefix is essential for understanding phenomena at a small scale, facilitating precise communication across microscopic and minuscule dimensions.