Weights and numbers are two different concepts, but they are often related in scientific usage.
- Weights are measures of the force of gravity acting on an object.
- Numbers are mathematical symbols that are used to represent quantities.
In scientific usage, the units of weight are units of mass. Mass is a measure of the amount of matter in an object. It is different from weight, which is a measure of the force of gravity acting on an object.
The most common unit of mass in scientific usage is the kilogram (kg). Other units of mass include the gram (g), the milligram (mg), and the microgram (µg).
Weights and numbers are often related in scientific usage because mass can be calculated from weight by dividing by the acceleration due to gravity (g). The acceleration due to gravity is a constant that varies slightly depending on location, but it is approximately 9.81 m/s^2 on Earth.
For example, an object with a mass of 1 kg weighs approximately 9.81 N on Earth. This can be calculated using the following equation:
weight = mass * g
where:
- weight is in newtons (N)
- mass is in kilograms (kg)
- g is the acceleration due to gravity (9.81 m/s^2)
Weights and numbers are used in many different scientific applications, including physics, chemistry, and engineering. For example, weights are used to measure the mass of objects in order to calculate their force, inertia, and momentum. Numbers are used to represent quantities such as distance, speed, and temperature.
Avoirdupoirs Weight
The avoirdupois weight system is a system of weights that is used for all goods except precious metals, stones, and medicines. It is the most common weight system used in the United States and the United Kingdom.
The basic unit of the avoirdupois weight system is the pound (lb). One pound is equal to 16 ounces (oz). One ounce is equal to 16 drams (dr).
The following table shows the units of the avoirdupois weight system in ascending order:
| Unit | Abbreviation | Equivalent |
|---|---|---|
| Dram | dr | 1/16 ounce |
| Ounce | oz | 1/16 pound |
| Pound | lb | 16 ounces |
| Stone | st | 14 pounds |
| Quarter | qr | 28 pounds |
| Hundredweight | cwt | 112 pounds |
| Ton | t | 20 hundredweight |
The avoirdupois weight system is used for a wide variety of goods, including food, clothing, building materials, and machinery. It is also used to measure the weight of people and animals.
Troy Weight
Troy weight is a system of units of mass that originated in 15th-century England and is primarily used in the precious metals industry. It is also used to weigh diamonds and pearls.
The troy weight system is based on the grain, which is equal to 0.0648 grams. The other units of troy weight are:
- Pennyweight (dwt): 24 grains
- Ounce: 20 pennyweights (480 grains)
- Pound: 12 ounces (373.27 grams)
Troy ounces and troy pounds are heavier than their avoirdupois counterparts. For example, a troy ounce is equal to 31.1035 grams, while an avoirdupois ounce is equal to 28.3495 grams.
Troy weight is used to weigh precious metals because it is a more precise system of measurement. Precious metals are often traded in very small quantities, so it is important to be able to measure their weight accurately.
Here is a table of the troy weight system:
| Unit | Grains | Grams |
|---|---|---|
| Grain | 1 | 0.0648 |
| Pennyweight (dwt) | 24 | 1.535 |
| Ounce | 480 | 31.1035 |
| Pound | 5760 | 373.27 |
Diamonds and pearls are weighed by carats, where one carat is equal to 4 grains. So, a 1-carat diamond weighs 0.2592 grams.
The purity of gold is measured in karats. Pure gold is said to be 24 karat fine. Gold that is mixed with other metals is said to be lower karat. For example, 18 karat gold is 75% gold and 25% other metals.
Troy weight is a complex system of measurement, but it is essential for the precious metals industry. It allows traders to accurately measure the weight of precious metals and to ensure that they are getting the value they pay for.
Apothecaries' Weight
The apothecaries' weight system is a traditional system of weight used for the measuring and dispensing of pharmaceutical items. It is based on the grain, scruple, dram, ounce, and pound. The grain is the smallest unit in the system, and is equal to 0.0648 grams. The scruple is equal to 20 grains, the dram is equal to 3 scruples, the ounce is equal to 8 drams, and the pound is equal to 12 ounces.
The apothecaries' weight system was developed in the Middle Ages, and was widely used in Europe and the Americas until the late 20th century. Today, it is still used in some countries, such as the United Kingdom and India.
Here is a table of the apothecaries' weight system:
| Unit | Symbol | Equivalent in grains | Equivalent in grams |
|---|---|---|---|
| Grain | gr | 1 | 0.0648 |
| Scruple | ℈ | 20 | 1.296 |
| Dram | dr | 60 | 3.888 |
| Ounce | oz | 480 | 31.1035 |
| Pound | lb | 5760 | 373.2417216 |
The apothecaries' weight system is important in pharmacy because it allows pharmacists to accurately measure and dispense drugs. Drugs are often dispensed in small quantities, such as milligrams or micrograms, so it is important to have a precise system of measurement. The apothecaries' weight system provides this precision.
Apothecaries' Fluid Measure
The apothecaries' fluid measure is a system of volume units used in pharmacy. It is based on the minim, which is a very small unit of volume, approximately equal to one drop. The apothecaries' fluid measure system is divided into the following units:
- Minim (m): The smallest unit in the apothecaries' fluid measure system, equal to about one drop of water.
- Fluid drachm (fÊ’): 60 minims.
- Fluid ounce (fl oz): 8 fluid drachms.
- Pint (O): 20 fluid ounces.
- Gallon (C): 8 pints.
The apothecaries' fluid measure system is still used in some countries, such as the United Kingdom and the United States. It is most commonly used in pharmacy and medicine to measure and dispense liquid medications.
Here is a table of the apothecaries' fluid measure system:
| Unit | Abbreviation | Equivalent in minims | Equivalent in centilitres | Equivalent in decilitres | Equivalent in litres |
|---|---|---|---|---|---|
| Minim | m | 1 | 0.0059 | 0.00059 | 0.000059 |
| Fluid drachm | fÊ’ | 60 | 0.355 | 0.0355 | 0.00355 |
| Fluid ounce | fl oz | 480 | 2.841 | 0.2841 | 0.002841 |
| Pint | O | 960 | 5.682 | 0.5682 | 0.005682 |
| Gallon | C | 7680 | 45.46 | 4.546 | 0.004546 |
Example:
A prescription for a medication might call for 1 teaspoon of liquid medication to be taken three times a day. One teaspoon is equal to approximately 5 millilitres. To dispense this medication, a pharmacist would use a graduated cylinder to measure out 5 millilitres of the medication. The pharmacist would then use a syringe to draw up the medication and dispense it to the patient.
British Measures of Length
| Measure | Unit | Abbr. | Feet | Yards | Meters |
|---|---|---|---|---|---|
| Linear Measure | Inch | in | 1 | 1/12 | 0.0254 |
| Linear Measure | Foot | ft | 12 | 1 | 0.3048 |
| Linear Measure | Yard | yd | 36 | 3 | 0.9144 |
| Linear Measure | Pole (rod) | pole | 5 1/2 | 1 1/2 | 5.0292 |
| Linear Measure | Chain | ch | 22 | 4 | 20.11678 |
| Linear Measure | Furlong | fur | 880 | 220 | 201.1678 |
| Linear Measure | Mile | mi | 5280 | 1760 | 1609.344 |
| Linear Measure | Nautical mile | nm | 6080 | 2026.667 | 1853.3 |
| Surveyors Measure | Link | lk | 1/24 | 1/792 | 0.201 |
| Surveyors Measure | Chain | ch | 100 | 25 | 20.11678 |
| Surveyors Measure | Mile | mi | 80 | 20 | 1609.344 |
| Surveyors Measure | Acre | ac | 10 sq ch | 4840 sq yds | 4046.8564224 |
Note that the Surveyor's mile is slightly shorter than the Linear mile, due to historical differences in measurement.
Square Measure
| Unit | Square Inches | Square Feet | Square Yards | Square Poles | Roods | Acres | Square Miles | Square Kilometers |
|---|---|---|---|---|---|---|---|---|
| Square Inch | 1 | 1/144 | 1/1296 | 1/39204 | 1/466560 | 1/5806080 | 1/70766400 | 0.000064516 |
| Square Foot | 144 | 1 | 1/9 | 1/30.5 | 1/4840 | 1/6272640 | 1/10117141.056 | 0.09290304 |
| Square Yard | 1296 | 9 | 1 | 1/3.55555555555556 | 1/5280 | 1/696960 | 1/10450113.2331233 | 0.83612736 |
| Square Pole | 39204 | 30.5 | 3.55555555555556 | 1 | 1/14.5238095238095 | 1/23310.7264 | 1/16018561.8331233 | 25.29285264 |
| Rood | 466560 | 4840 | 5280 | 14.5238095238095 | 1 | 1/4 | 1/102400 | 1011.7141056 |
| Acre | 5806080 | 6272640 | 696960 | 23310.7264 | 4 | 1 | 1/640 | 4046.8564224 |
| Square Mile | 70766400 | 10117141.056 | 10450113.2331233 | 16018561.8331233 | 102400 | 640 | 1 | 2589988.110336 |
Solid or Cubic Measure
| Unit | Conversion Factor | Equivalent |
|---|---|---|
| 178 Cubic inches | 0.00292 Cubic meter | 2920 Cubic centimeters |
| 1 Cubic foot | 0.0283 Cubic meter | 28,316.846592 Cubic centimeters |
| 2 Cubic feet | 1 Register Ton | 0.765 Cubic meter |
| 100 Cubic feet | 1 Register Ton | 2.832 Cubic meter |
Conversions
- 178 Cubic inches to Cubic meter: 178 Cubic inches * 0.00292 Cubic meter/Cubic inch = 0.00292 Cubic meter
- 1 Cubic foot to Cubic meter: 1 Cubic foot * 0.0283 Cubic meter/Cubic foot = 0.0283 Cubic meter
- 2 Cubic feet to Register Ton: 2 Cubic feet * 1 Register Ton/2 Cubic feet = 1 Register Ton
- 100 Cubic feet to Register Ton: 100 Cubic feet * 1 Register Ton/100 Cubic feet = 1 Register Ton
Note:
- 1 Register Ton is a unit of volume used in shipping and is equal to 40 cubic feet.
- The cubic meter is the standard unit of volume in the International System of Units (SI).