Measures of length
| Unit | Abbreviation | Equal to |
|---|---|---|
| Millimeter | mm | 0.001 meters |
| Centimeter | cm | 0.01 meters |
| Meter | m | 1 meter |
| Kilometer | km | 1,000 meters |
Square measure
- kilo- (k): 1,000 times larger
- hecto- (h): 100 times larger
- deka- (da): 10 times larger
- **** (no prefix):** base unit
- deci- (d): 10 times smaller
- centi- (c): 100 times smaller
- milli- (m): 1,000 times smaller
| Unit | Symbol | Definition |
|---|---|---|
| square kilometer | km² | 1,000,000 square meters |
| hectare | ha | 10,000 square meters |
| are | a | 100 square meters |
| square meter | m² | Base unit |
| square decimeter | dm² | 0.01 square meters |
| square centimeter | cm² | 0.0001 square meters |
| square millimeter | mm² | 0.000001 square meters |
Square measure is used to measure the area of a variety of objects, including land, buildings, and objects. For example, the area of a rectangular garden that is 10 meters long and 5 meters wide is 50 square meters (10 meters × 5 meters = 50 square meters).
Cubic Measure
Multiples and Submultiples of Cubic Meters
Cubic meters can be divided into smaller units using prefixes. The most common prefixes used with cubic meters are:
- kilo- (k): 1000 cubic meters
- hecto- (h): 100 cubic meters
- deca- (da): 10 cubic meters
- deci- (d): 0.1 cubic meters
- centi- (c): 0.01 cubic meters
- milli- (m): 0.001 cubic meters
Examples of Cubic Measure
- A swimming pool has a volume of 1000 cubic meters.
- A box of cereal has a volume of 0.001 cubic meters.
- A cubic centimeter is equal to 0.000001 cubic meters.
- Converting Cubic Meters to Other Units of Volume
Cubic meters can be converted to other units of volume using the following conversion factors:
- 1 cubic meter is equal to 1000 liters
- 1 cubic meter is equal to 35.3147 cubic feet
- 1 cubic meter is equal to 1.30795 cubic yards
Applications of Cubic Measure
Cubic measure is used in a wide variety of applications, including:
Architecture and engineering: Cubic measure is used to calculate the volume of buildings, rooms, and other structures.
Construction: Cubic measure is used to calculate the volume of concrete, asphalt, and other materials.
Shipping and transportation: Cubic measure is used to calculate the volume of cargo containers and other shipping vessels.
Science and engineering: Cubic measure is used to calculate the volume of gases, liquids, and solids.
Measures of time
- Millisecond (ms): 1/1000 of a second
- Microsecond (µs): 1/1,000,000 of a second
- Nanosecond (ns): 1/1,000,000,000 of a second
- Minute (min): 60 seconds
- Hour (h): 60 minutes
- Day (d): 24 hours
Measures of Capacity
Capacity is a measure of the volume of a container or object. In the metric system, the base unit of capacity is the liter (L). One liter is equal to 1 cubic decimeter (dm³).
There are also smaller and larger units of capacity, which are based on the liter. These units are related to each other by factors of 10. For example, one milliliter (mL) is equal to one-thousandth of a liter, and one kiloliter (kL) is equal to one thousand liters.
Here is a table of the metric units of capacity:
| Unit | Symbol | Definition |
|---|---|---|
| Milliliter | mL | 1 mL = 0.001 L |
| Centiliter | cL | 1 cL = 0.1 L |
| Deciliter | dL | 1 dL = 1 L |
| Liter | L | 1 L = 1 dm³ |
| Decaliter | daL | 1 daL = 10 L |
| Hectoliter | hL | 1 hL = 100 L |
| Kiloliter | kL | 1 kL = 1000 L |
Examples of Measures of Capacity
- A glass of water is about 250 mL.
- A bottle of soda is about 355 mL.
- A gallon of milk is about 3.785 L.
- A swimming pool is about 10,000 L.
- A tanker truck can hold up to 30,000 L of gasoline.
Converting Measures of Capacity
To convert between metric units of capacity, you can use the following rule:
1 unit = 10 × (the next smaller unit)
For example, to convert 1 liter to milliliters, you would use the following equation:
1 L = 10 × mL
This means that 1 liter is equal to 1000 milliliters.
To convert between metric and non-metric units of capacity, you can use a conversion table.
Paper Measures
In the metric system, paper is measured in millimeters (mm) and centimeters (cm). An A4 sheet of paper is 210 mm × 297 mm.
| Size | Width (mm) | Height (mm) |
|---|---|---|
| A0 | 841 | 1189 |
| A1 | 594 | 841 |
| A2 | 420 | 594 |
| A3 | 297 | 420 |
| A4 | 210 | 297 |
| A5 | 148 | 210 |
| A6 | 105 | 148 |
| A7 | 74 | 105 |
| A8 | 52 | 74 |
| A9 | 37 | 52 |
| A10 | 26 | 37 |
Temperatureas - Centigrade and Fahrenheit
Temperature is a measure of how hot or cold something is. It is measured in degrees Celsius (°C) in the metric system. The Celsius scale is based on the freezing and boiling points of water, with 0°C being the freezing point and 100°C being the boiling point.
In the United States, temperature is still often measured in degrees Fahrenheit (°F). The Fahrenheit scale is based on the freezing and boiling points of brine (a mixture of salt and water), with 32°F being the freezing point and 212°F being the boiling point.
To convert between Celsius and Fahrenheit, you can use the following formulas:
- Celsius to Fahrenheit: °F = (°C × 9/5) + 32
- Fahrenheit to Celsius: °C = (°F − 32) × 5/9
Why the United States still uses Fahrenheit?
There are a number of reasons why the United States still uses Fahrenheit, including:
- History: The Fahrenheit scale was first introduced in the early 18th century, and it has been used in the United States ever since.
- Tradition: Many people in the United States are familiar with Fahrenheit, and they are reluctant to change to a new system.
- Cost: It would be expensive to convert all of the measuring devices in the United States to the metric system.
However, there is a growing movement in the United States to switch to the metric system. Many businesses and organizations have already made the switch, and the government is also considering making the metric system the official system of measurement in the United States.
Roman Numerals
Roman numerals are a system of numerical notation that was developed in ancient Rome. Roman numerals are based on the symbols I, V, X, L, C, D, and M, which represent the numbers 1, 5, 10, 50, 100, 500, and 1,000, respectively.
Mmost common Roman numerals:
| Roman Numeral | Value |
|---|---|
| I | 1 |
| II | 2 |
| III | 3 |
| IV | 4 |
| V | 5 |
| VI | 6 |
| VII | 7 |
| VIII | 8 |
| IX | 9 |
| X | 10 |
| XI | 11 |
| XII | 12 |
| XIII | 13 |
| XIV | 14 |
| XV | 15 |
| XVI | 16 |
| XVII | 17 |
| XVIII | 18 |
| XIX | 19 |
| XX | 20 |
Roman numerals are no longer in common use, but they are still used in some places, such as on clocks and watches and in some formal documents.
Here are some of the Indian units of measurement that are still in use:
- Lakh: A lakh is equal to 100,000.
- Million: A million is equal to 1,000,000.
- Crore: A crore is equal to 10,000,000.
- Billion: A billion is equal to 1,000,000,000.
- Trillion: A trillion is equal to 1,000,000,000,000.
- TMC (thousand million crore): A tmc is equal to 1,000,000,000,000,000.
Measurement of discharge of water from reservoirs
The discharge of water from a reservoir is the rate at which water is flowing out of the reservoir. It is measured in cubic meters per second (m³/s). There are a number of different methods that can be used to measure the discharge of water from a reservoir, including:
Weirs and flumes: Weirs and flumes are structures that are placed in the outlet of a reservoir to measure the flow of water. They work by creating a constriction in the flow of water, which causes the water level to rise. The height of the water level is then used to calculate the discharge of water.
Current meters: Current meters are devices that are used to measure the velocity of water flowing in a stream. They are typically used to measure the discharge of water from small reservoirs or streams.
Acoustic Doppler velocimeters (ADVs): ADVs are devices that use sound waves to measure the velocity of water flowing in a stream. They are typically used to measure the discharge of water from large reservoirs or rivers.
The choice of method for measuring the discharge of water from a reservoir will depend on a number of factors, including the size of the reservoir, the accuracy required, and the cost of the equipment.
Measurement of power
Power is the rate at which work is done. It is typically measured in watts (W). One watt is equal to one joule per second (J/s).
There are a number of different units of power, including:
- Watt (W)
- Kilowatt (kW)
- Megawatt (MW)
- Gigawatt (GW)
- Terawatt (TW)
- Petawatt (PW)
One kilowatt is equal to 1,000 watts. One megawatt is equal to 1,000 kilowatts. One gigawatt is equal to 1,000 megawatts. One terawatt is equal to 1,000 gigawatts. One petawatt is equal to 1,000 terawatts.
Absolute temperature
Absolute temperature is a measure of temperature on a scale that has zero at absolute zero. Absolute zero is the lowest possible temperature, at which the motion of particles stops. The Kelvin scale is the absolute temperature scale, and it is used in science and engineering.
The Kelvin scale is defined so that one Kelvin is equal to 1/273.16 of the thermodynamic temperature of the triple point of water. The triple point of water is the temperature and pressure at which water can exist in all three phases: solid, liquid, and gas.
Absolute zero
Absolute zero is the lowest possible temperature, at which the motion of particles stops. It is equal to -273.15 degrees Celsius (°C) or -459.67 degrees Fahrenheit (°F).
At absolute zero, there is no internal energy, and the particles are stationary. This means that there is no entropy, or disorder, in the system.
Absolute zero is unattainable in practice, but it is a useful theoretical concept. It is used in many areas of science, including thermodynamics, statistical mechanics, and quantum mechanics.
Mathematical signs
Mathematical signs are symbols that are used to represent operations, such as addition, subtraction, multiplication, and division. Some common mathematical signs include:
- + (plus): Addition
- - (minus): Subtraction
- × (multiply): Multiplication
- ÷ (divide): Division
- = (equals): Equality
- ≠ (not equals):** Inequality
- < (less than):** Less than
- (greater than):** Greater than
- ≤ (less than or equal to):** Less than or equal to
- ≥ (greater than or equal to):** Greater than or equal to
Mathematical signs are also used to represent other concepts, such as variables, constants, and functions.
Number of Days in Each Month
There are 12 months in a year, and the number of days in each month varies. Here is a table of the number of days in each month:
| Month | Number of Days |
|---|---|
| January | 31 |
| February | 28 (or 29 in a leap year) |
| March | 31 |
| April | 30 |
| May | 31 |
| June | 30 |
| July | 31 |
| August | 31 |
| September | 30 |
| October | 31 |
| November | 30 |
| December | 31 |
To determine whether a year is a leap year, divide the year by 4. If the remainder is 0, then the year is a leap year.
Table of Numbers
- Articles: An article is a single item, such as a pen, a book, or a piece of fruit.
- Dozen: A dozen is a group of 12 articles. For example, 12 pens, 12 books, or 12 pieces of fruit make a dozen.
- Gross: A gross is a group of 12 dozen, or a total of 144 articles. For example, 12 dozen pens, 12 dozen books, or 12 dozen pieces of fruit make a gross.
- Score: A score is a group of 20 articles. For example, 20 pens, 20 books, or 20 pieces of fruit make a score.
- Hundred: A hundred is a group of 5 scores, or a total of 100 articles. For example, 5 scores of pens, 5 scores of books, or 5 scores of pieces of fruit make a hundred.
| Quantity | Number of articles |
|---|---|
| Article | 1 |
| Dozen | 12 |
| Gross | 144 |
| Score | 20 |
| Hundred | 100 |