Question

Write the symbol for the following metric units. (a) terameter (b) gigagram (c) nanoliter (d) picosecond

Short answer

(a) Tm, (b) Gg, (c) nL, (d) ps.

Step-by-step solution

Understand Metric Prefixes

Metric units are often used with different prefixes that denote specific powers of ten. Each prefix corresponds to a specific power of ten and has a distinct symbol. For example, 'tera-' means a trillion (\(10^{12}\)), 'giga-' means a billion (\(10^{9}\)), 'nano-' means a billionth (\(10^{-9}\)), and 'pico-' means a trillionth (\(10^{-12}\)).

Write the Symbol for Terameter

The 'tera-' prefix stands for \(10^{12}\) and is denoted by 'T'. The base unit 'meter' is denoted by 'm'. Therefore, the symbol for terameter is 'Tm'.

Write the Symbol for Gigagram

The 'giga-' prefix stands for \(10^{9}\) and is denoted by 'G'. The base unit 'gram' is denoted by 'g'. Therefore, the symbol for gigagram is 'Gg'.

Write the Symbol for Nanoliter

The 'nano-' prefix stands for \(10^{-9}\) and is denoted by 'n'. The base unit 'liter' is denoted by 'L'. Therefore, the symbol for nanoliter is 'nL'.

Write the Symbol for Picosecond

The 'pico-' prefix stands for \(10^{-12}\) and is denoted by 'p'. The base unit 'second' is denoted by 's'. Therefore, the symbol for picosecond is 'ps'.

Key concepts

Metric Units

Metric units are a standardized system of measurement. They are widely used in science and everyday life for their consistency. The metric system is based on base units combined with prefixes. A base unit stands for a fundamental quantity like length, mass, or volume. You probably know some base units, such as:

• Meter (m) - used for measuring length
• Gram (g) - used for measuring mass
• Liter (L) - used for measuring volume
• Second (s) - used for measuring time

To express large or tiny quantities easily, metric prefixes are added to these base units. These prefixes represent powers of ten, making it easier to read and understand numbers. For example, a kilometer (km) is 1000 meters.

Powers of Ten

Powers of ten are essential to understanding metric prefixes. They help us translate numeric expressions into simpler terms using powers. Here's how powers of ten work:- Any number can be written in terms of ten raised to an exponent. For example, 1000 can be written as \(10^3\).- The exponent indicates how many times to multiply ten by itself.- Positive exponents like \(10^2\) (which equals 100) signify numbers larger than one.- Negative exponents like \(10^{-3}\) (which equals 0.001) are used for numbers smaller than one.Using powers of ten with metric units simplifies the notation of very large or very tiny numbers. For instance, a gigabyte involves \(10^9\) bytes, showcasing the convenience of this system.

Scientific Notation

Scientific notation is a way to express very large or small numbers in a concise form. It combines the power of ten with a decimal value to make multiplication easier. Here's how scientific notation works:

• A number is expressed as the product of a number between 1 and 10, and a power of ten.
• For instance, the number 4,500 can be rewritten as \(4.5 \times 10^3\).
• This form is particularly useful in science and engineering, where you often deal with extreme values.

Metric prefixes in scientific notation make interpreting scientific data straightforward. Researchers and engineers use scientific notation for clarity, as it enables them to recognize at a glance how large or small a quantity is without parsing a string of zeros. This notation integrates seamlessly with metric units.