Question

State the name and symbol for the metric prefix that represents the following: (a) \(1 \times 10^{12}\) (b) \(1 \times 10^{9}\) (c) \(1 \times 10^{-3}\) (d) \(1 \times 10^{-6}\)

Short answer

(a) tera (T), (b) giga (G), (c) milli (m), (d) micro (µ).

Step-by-step solution

Understanding Metric Prefixes

Metric prefixes are used in the metric system to denote powers of ten. Each prefix has a unique name and symbol. For example, the prefix for \(10^3\) is 'kilo' with the symbol 'k'.

Identify the Prefix for \(1 \times 10^{12}\)

The metric prefix for \(10^{12}\) is 'tera'. The symbol for tera is 'T'. Therefore, the name and symbol for \(1 \times 10^{12}\) is tera (T).

Identify the Prefix for \(1 \times 10^{9}\)

The metric prefix for \(10^{9}\) is 'giga'. The symbol for giga is 'G'. Thus, the name and symbol for \(1 \times 10^{9}\) is giga (G).

Identify the Prefix for \(1 \times 10^{-3}\)

For \(10^{-3}\), the metric prefix is 'milli'. Its symbol is 'm'. Hence, the name and symbol for \(1 \times 10^{-3}\) is milli (m).

Identify the Prefix for \(1 \times 10^{-6}\)

The metric prefix for \(10^{-6}\) is 'micro'. The symbol used for micro is 'µ'. Therefore, the name and symbol for \(1 \times 10^{-6}\) is micro (µ).

Key concepts

Understanding Tera

Tera is a metric prefix in the International System of Units (SI) that stands for one trillion or \(10^{12}\). It is symbolized by the letter 'T'. This prefix is often used in contexts where large measurements of data are common, such as in computing. For instance:

• 1 terabyte (TB) = 1,000 gigabytes (GB) = \(1 \times 10^{12}\) bytes
• 1 terahertz (THz) refers to frequencies equating to \(1 \times 10^{12}\) cycles per second

Tera provides a useful way to express very large quantities without using cumbersome and lengthy numerical forms. When dealing with large-scale data projects or high-frequency signals, recognizing the tera prefix allows you to easily understand the orders of magnitude involved.

Understanding Giga

Giga denotes a billion, or \(10^9\), and its symbol is 'G'. This prefix is widely used in everyday technology language, especially in the realm of digital storage and computing:

• 1 gigabyte (GB) = \(1 \times 10^{9}\) bytes
• 1 gigahertz (GHz) represents a frequency of a billion cycles per second

Using giga helps simplify communication by aggregating large quantities into manageable figures. Whether you're upgrading a computer or analyzing data speeds, the giga prefix forms an integral part of understanding these concepts, making them more accessible and less intimidating.

Understanding Milli

Milli is a metric prefix that translates to \(10^{-3}\) or one-thousandth. It's represented by the letter 'm'. This prefix often appears in contexts where precision is crucial, particularly in measurements of length, volume, or other dimensions:

• 1 millimeter (mm) = \(1 \times 10^{-3}\) meters
• 1 milliliter (mL) = \(1 \times 10^{-3}\) liters

By using the milli prefix, vast or intricate concepts can be broken down into smaller, more intuitive subunits that enhance understanding and application. Particularly in scientific and engineering fields, precision is critical, and milli provides a convenient way to express minute quantities effectively.

Understanding Micro

Micro is another metric prefix representing \(10^{-6}\), or one-millionth, and is symbolized by the Greek letter 'µ'. This prefix is prominently used in science and technology, especially when discussing small units like:

• 1 micrometer (µm) = \(1 \times 10^{-6}\) meters, crucial in fields like microbiology and materials science
• 1 microsecond (µs) = \(1 \times 10^{-6}\) seconds, useful in electronics and time-sensitive applications like oscilloscopes

The micro prefix allows scientists and engineers to express tiny measurements or time intervals clearly, promoting understanding even in complex scenarios. This facilitates a clear grasp of scales and dimensions that are too small to be described conveniently in standard units, thus aiding in accurate communication and analysis.