Question

Write the complete name for each of the following units: a. \(\mathrm{cm}\) b. \(\mathrm{ks}\) c. \(\mathrm{dL}\) d. Gm e. \(\mu \mathrm{g}\) f. \(\mathrm{pg}\)

Short answer

cm: centimeter; ks: kilosecond; dL: deciliter; Gm: gigameter; μg: microgram; pg: picogram.

Step-by-step solution

Identify the unit for \(\text{cm}\)

The abbreviation \(\text{cm}\) stands for centimeter, which is a unit of length in the metric system. It is derived from the base unit 'meter' with the prefix 'centi-' indicating a factor of \(10^{-2}\).

Identify the unit for \(\text{ks}\)

The abbreviation \(\text{ks}\) stands for kilosecond, a unit of time. The prefix 'kilo-' indicates a factor of \ (10^3) \, so 1 kilosecond equals 1,000 seconds.

Identify the unit for \(\text{dL}\)

The abbreviation \(\text{dL}\) stands for deciliter, which is a unit of volume. The prefix 'deci-' indicates a factor of \(10^{-1}\), thus 1 deciliter equals 0.1 liters.

Identify the unit for Gm

The abbreviation Gm stands for gigameter, a unit of length. The prefix 'giga-' indicates a factor of \(10^9\), so 1 gigameter equals 1,000,000,000 meters.

Identify the unit for \(\text{μg}\)

The abbreviation \(\text{μg}\) stands for microgram, a unit of mass. The prefix 'micro-' denotes a factor of \(10^{-6}\), making 1 microgram equal to \(10^{-6}\) grams.

Identify the unit for \(\text{pg}\)

The abbreviation \(\text{pg}\) stands for picogram, another unit of mass. The prefix 'pico-' represents a factor of \(10^{-12}\), so 1 picogram is \(10^{-12}\) grams.

Key concepts

centimeter

A centimeter is a unit of length in the metric system. The prefix 'centi-' indicates that it is one hundredth of a meter, or \(\frac{1}{100} \) of a meter. This means that 1 centimeter (cm) equals 0.01 meters (m). Typically, centimeters are used to measure shorter distances, like the length of a pencil or the width of a book. Conversion between centimeters and meters is simple: multiply or divide by 100.

• 1 cm = 0.01 m
• 100 cm = 1 m

kilosecond

A kilosecond is a unit of time that equals 1,000 seconds. The prefix 'kilo-' indicates a factor of \(10^3 \). This unit is not commonly used in everyday life but can be useful in specific scientific contexts where larger time intervals need to be measured without using hours or minutes.

• 1 kilosecond (ks) = 1,000 seconds
• 1000 kiloseconds = 1,000,000 seconds

deciliter

A deciliter is a unit of volume and is equal to one-tenth of a liter. The prefix 'deci-' indicates a factor of \(10^{-1}\). This means that 1 deciliter (dL) equals 0.1 liters (L). Deciliters are frequently used in cooking and in nutritional contexts, especially in Europe.

• 1 dL = 0.1 L
• 10 dL = 1 L

gigameter

A gigameter is a unit of length that equals one billion meters. The prefix 'giga-' denotes a factor of \(10^9 \), so 1 gigameter (Gm) equals 1,000,000,000 meters. This unit is mostly used in scientific contexts, such as astronomy, to measure enormous distances. Conversion between gigameters and meters involves multiplying or dividing by one billion.

• 1 Gm = 1,000,000,000 m
• 0.1 Gm = 100,000,000 m

microgram

A microgram is a unit of mass equal to one-millionth of a gram. The prefix 'micro-' signifies a factor of \(10^{-6} \). This small unit is often used in fields like pharmacology and biology to measure minute quantities of substances. For example, the recommended daily intake of certain vitamins might be measured in micrograms.

• 1 μg = \(10^{-6} \) grams
• 1,000,000 μg = 1 gram

picogram

A picogram is an even smaller unit of mass than a microgram, equal to one-trillionth of a gram. The prefix 'pico-' indicates a factor of \(10^{-12} \). Picograms are used in specialized scientific fields where extremely tiny measurements are needed, such as in molecular biology and nanotechnology.

• 1 pg = \(10^{-12} \) grams
• 1,000,000,000,000 pg = 1 gram