Question

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

Short answer

(a) mega (M), (b) kilo (k), (c) nano (n), (d) pico (p)

Step-by-step solution

Identify the Metric Prefix for 10^6

The metric prefix for \(1 \times 10^{6}\) is 'mega', which is represented by the symbol 'M'. So, \(1 \times 10^{6} = \text{M (mega)}\).

Identify the Metric Prefix for 10^3

The metric prefix for \(1 \times 10^{3}\) is 'kilo', which is represented by the symbol 'k'. Thus, \(1 \times 10^{3} = \text{k (kilo)}\).

Identify the Metric Prefix for 10^-9

The metric prefix for \(1 \times 10^{-9}\) is 'nano', and it is represented by the symbol 'n'. Therefore, \(1 \times 10^{-9} = \text{n (nano)}\).

Identify the Metric Prefix for 10^-12

The metric prefix for \(1 \times 10^{-12}\) is 'pico', with the symbol 'p'. Thus, \(1 \times 10^{-12} = \text{p (pico)}\).

Key concepts

Mega - The Million Multiplier

In the metric system, the prefix "mega" represents a factor of one million, or \( 1 \times 10^6 \). It is denoted by the symbol "M". This means that whenever you see "Mega" before a unit, you should think about multiplying that unit by a million.
For example, 1 Megawatt (MW) means 1,000,000 watts. This is helpful in industries like power generation where energy values are high and using plain numbers without prefixes can be cumbersome.

• Mega is used for large quantities.
• Helps to simplify numbers by reducing zeros.
• Commonly seen in terms like megabytes (MB) in computing.

Whether talking about data storage, power, or quantities, "Mega" efficiently conveys massive numbers in a compact form.

Kilo - The Thousand Multiplier

The metric prefix "kilo" stands for one thousand, or \( 1 \times 10^3 \). It is symbolized by a lowercase "k". This prefix is frequently used in daily life, especially when dealing with measurements like mass and distance. For example, 1 kilogram (kg) equals 1,000 grams.
In technology, you see "kilo" in terms like kilobyte (kB), which equates to 1,000 bytes, though technically (and confusingly) 1 kB is often equated to 1,024 bytes due to binary system usage in computing.

• Kilo helps bridge the gap between small units and practical everyday quantities.
• Pervades domains like computing, physics, and geography.
• Eases communication by simplifying numeric representations.

This prefix is a cornerstone in creating understandable and usable data and measurement numbers.

Nano - The Billionth Divider

"Nano" is a prefix in the metric system indicating a factor of \( 10^{-9} \), or one-billionth. Represented by the symbol "n", nano is often associated with incredibly small measurements, often seen in scientific fields.
In technology, for instance, 1 nanometer (nm) equals one-billionth of a meter. This scale is crucial in fields like nanotechnology and electronics, where researchers work on materials and components at atomic and molecular levels.

• Nano is vital for exploring microscopic and atomic dimensions.
• Has revolutionized fields like electronics, biology, and medicine.
• Enables advancements in smart technology and materials science.

The "nano" scale allows scientists and engineers to develop technologies with precision and detail unimaginable at regular scales.

Pico - The Trillionth Divider

The prefix "pico" denotes a factor of \( 10^{-12} \), or one-trillionth, in the metric system. Shown by the symbol "p", pico is used for ultra-small measurements that are crucial in certain scientific fields.
A picosecond, which is one trillionth of a second, is a common term in physics, especially when measuring the time it takes light to travel certain tiny distances. In chemistry, concentrations of substances may be given in picomoles.

• Pico helps in studying and measuring phenomena that operate on incredibly short timescales and small amounts.
• Key in high precision engineering and scientific research.
• Used in fields like optics, quantum computing, and life sciences.

This level of measurement sophistication allows us to engage with the natural world on incredibly detailed scales, discovering new scientific frontiers.