### Maths Metric System

##### Metric System

The metric system is a system of measurement that is based on the decimal system. It was developed in France in the late 18th century and is now the most widely used system of measurement in the world.

##### Base Units

The metric system is based on seven base units:

**Meter (m)**: The meter is the unit of length. It is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second.**Kilogram (kg)**: The kilogram is the unit of mass. It is defined as the mass of a specific platinum-iridium cylinder that is kept at the International Bureau of Weights and Measures in France.**Second (s)**: The second is the unit of time. It is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two levels of the cesium-133 atom.**Ampere (A)**: The ampere is the unit of electric current. It is defined as the amount of current that flows through a conductor when one volt is applied across it and the resistance is one ohm.**Kelvin (K)**: The kelvin is the unit of thermodynamic temperature. It is defined as 1/273.16 of the thermodynamic temperature of the triple point of water.**Mole (mol)**: The mole is the unit of amount of substance. It is defined as the amount of substance that contains exactly 6.02214076×10$^{23}$ elementary entities (such as atoms, molecules, ions, or electrons).**Candela (cd)**: The candela is the unit of luminous intensity. It is defined as the luminous intensity of a source that emits monochromatic radiation of frequency $540×10^{12}$ hertz and has a radiant intensity in that direction of 1/683 watt per steradian.

##### Prefixes

The metric system uses a series of prefixes to indicate multiples and submultiples of the base units. These prefixes are:

**Yotta (Y)**: $10^{24}$**Zetta (Z)**: $10^{21}$**Exa (E)**: $10^{18}$**Peta (P)**: $10^{15}$**Tera (T)**: $10^{12}$**Giga (G)**: $10^{9}$**Mega (M)**: $10^{6}$**Kilo (k)**: $10^{3}$**Hecto (h)**: $10^{2}$**Deka (da)**: $10^{1}$**Deci (d)**: $10^{-1}$**Centi (c)**: $10^{-2}$**Milli (m)**: $10^{-3}$**Micro (µ)**: $10^{-6}$**Nano (n)**: $10^{-9}$**Pico (p)**: $10^{-12}$**Femto (f)**: $10^{-15}$**Atto (a)**: $10^{-18}$**Zepto (z)**: $10^{-21}$**Yocto (y)**: $10^{-24}$

##### Metric System Units

The metric system is a decimal system of measurement that is based on the meter, kilogram, and second. It is the most widely used system of measurement in the world, and it is used in all scientific work.

##### Base Units

The metric system has seven base units, which are:

**Meter (m)**: The meter is the unit of length. It is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second.**Kilogram (kg)**: The kilogram is the unit of mass. It is defined as the mass of a specific platinum-iridium cylinder that is kept at the International Bureau of Weights and Measures in France.**Second (s)**: The second is the unit of time. It is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two levels of the cesium-133 atom.**Ampere (A)**: The ampere is the unit of electric current. It is defined as the flow of one coulomb of charge per second.**Kelvin (K)**: The kelvin is the unit of thermodynamic temperature. It is defined as 1/273.16 of the thermodynamic temperature of the triple point of water.**Mole (mol)**: The mole is the unit of amount of substance. It is defined as the amount of substance that contains exactly 6.02214076×10^23 elementary entities.**Candela (cd)**: The candela is the unit of luminous intensity. It is defined as the luminous intensity of a source that emits monochromatic radiation of frequency 540×10^12 hertz with a radiant intensity of 1/683 watt per steradian.

##### Derived Units

In addition to the base units, the metric system also has a number of derived units, which are units that are defined in terms of the base units. Some of the most common derived units include:

**Newton (N)**: The newton is the unit of force. It is defined as the force that produces an acceleration of 1 meter per second squared on a mass of 1 kilogram.**Joule (J)**: The joule is the unit of energy. It is defined as the work done by a force of 1 newton acting through a distance of 1 meter.**Watt (W)**: The watt is the unit of power. It is defined as the rate at which work is done, and it is equal to 1 joule per second.**Pascal (Pa)**: The pascal is the unit of pressure. It is defined as the pressure exerted by a force of 1 newton acting on an area of 1 square meter.**Hertz (Hz)**: The hertz is the unit of frequency. It is defined as the number of cycles per second.

##### Advantages of the Metric System

The metric system has a number of advantages over other systems of measurement, including:

**It is a decimal system**, which makes it easy to convert between units.**It is based on natural phenomena**, which makes it more consistent and accurate than other systems of measurement.**It is the most widely used system of measurement in the world**, which makes it easier to communicate with people from other countries.

The metric system is the most widely used system of measurement in the world, and it is the system of measurement that is used in all scientific work. It is a decimal system that is based on natural phenomena, and it is easy to convert between units.

##### Metric System Prefixes

The metric system is a decimal system of measurement that is based on the meter, kilogram, and second. It is the most widely used system of measurement in the world.

The metric system uses a series of prefixes to indicate multiples and submultiples of the base units. These prefixes are based on powers of 10.

##### Prefixes for Multiples

Prefix | Symbol | Multiple |
---|---|---|

kilo | k | 10^{3} |

mega | M | 10^{6} |

giga | G | 10^{9} |

tera | T | 10^{12} |

peta | P | 10^{15} |

exa | E | 10^{18} |

zetta | Z | 10^{21} |

yotta | Y | 10^{24} |

##### Prefixes for Submultiples

Prefix | Symbol | Submultiple |
---|---|---|

milli | m | 10^{-3} |

micro | µ | 10^{-6} |

nano | n | 10^{-9} |

pico | p | 10^{-12} |

femto | f | 10^{-15} |

atto | a | 10^{-18} |

zepto | z | 10^{-21} |

yocto | y | 10^{-24} |

##### Examples

Here are some examples of how metric system prefixes are used:

- A kilometer is 1000 meters.
- A megabyte is 1,000,000 bytes.
- A nanosecond is 0.000000001 seconds.

The metric system is a powerful tool for measuring the world around us. The use of prefixes makes it easy to express very large and very small numbers in a convenient and understandable way.

##### Metric System Conversion Chart

The metric system is a system of measurement based on the decimal system. It is the most widely used system of measurement in the world.

The metric system is based on seven base units:

- Meter (m): The unit of length
- Kilogram (kg): The unit of mass
- Second (s): The unit of time
- Ampere (A): The unit of electric current
- Kelvin (K): The unit of thermodynamic temperature
- Mole (mol): The unit of amount of substance
- Candela (cd): The unit of luminous intensity

##### Length

Metric Unit | Equivalent in SI Base Units |
---|---|

Kilometer (km) | 1,000 meters |

Hectometer (hm) | 100 meters |

Dekameter (dam) | 10 meters |

Meter (m) | 1 meter |

Decimeter (dm) | 0.1 meters |

Centimeter (cm) | 0.01 meters |

Millimeter (mm) | 0.001 meters |

Micrometer (µm) | 0.000001 meters |

Nanometer (nm) | 0.000000001 meters |

Picometer (pm) | 0.000000000001 meters |

##### Mass

Metric Unit | Equivalent in SI Base Units |
---|---|

Tonne (t) | 1,000 kilograms |

Quintal (q) | 100 kilograms |

Kilogram (kg) | 1 kilogram |

Hectogram (hg) | 100 grams |

Dekagram (dag) | 10 grams |

Gram (g) | 1 gram |

Decigram (dg) | 0.1 grams |

Centigram (cg) | 0.01 grams |

Milligram (mg) | 0.001 grams |

Microgram (µg) | 0.000001 grams |

Nanogram (ng) | 0.000000001 grams |

Picogram (pg) | 0.000000000001 grams |

##### Time

Metric Unit | Equivalent in SI Base Units |
---|---|

Day (d) | 86,400 seconds |

Hour (h) | 3,600 seconds |

Minute (min) | 60 seconds |

Second (s) | 1 second |

Millisecond (ms) | 0.001 seconds |

Microsecond (µs) | 0.000001 seconds |

Nanosecond (ns) | 0.000000001 seconds |

Picosecond (ps) | 0.000000000001 seconds |

##### Temperature

Metric Unit | Equivalent in SI Base Units |
---|---|

Degree Celsius (°C) | Kelvin - 273.15 |

Kelvin (K) | 1 Kelvin |

##### Volume

Metric Unit | Equivalent in SI Base Units |
---|---|

Liter (L) | 0.001 cubic meters |

Deciliter (dL) | 0.1 liters |

Centiliter (cL) | 0.01 liters |

Milliliter (mL) | 0.001 liters |

Microliter (µL) | 0.000001 liters |

Nanoliter (nL) | 0.000000001 liters |

Picoliter (pL) | 0.000000000001 liters |

##### Area

Metric Unit | Equivalent in SI Base Units |
---|---|

Square kilometer (km²) | 1,000,000 square meters |

Hectare (ha) | 10,000 square meters |

Are (a) | 100 square meters |

Square meter (m²) | 1 square meter |

Square decimeter (dm²) | 0.01 square meters |

Square centimeter (cm²) | 0.0001 square meters |

Square millimeter (mm²) | 0.000001 square meters |

Square micrometer (µm²) | 0.000000000001 square meters |

Square nanometer (nm²) | 0.000000000000000001 square meters |

Square picometer (pm²) | 0.0000000000000000000001 square meters |

##### Speed

Metric Unit | Equivalent in SI Base Units |
---|---|

Kilometer per hour (km/h) | 0.277778 meters per second |

Meter per second (m/s) | 1 meter per second |

Centimeter per second (cm/s) | 0.01 meters per second |

Millimeter per second (mm/s) | 0.001 meters per second |

Micrometer per second (µm/s) | 0.000001 meters per second |

Nanometer per second (nm/s) | 0.000000001 meters per second |

Picometer per second (pm/s) | 0.000000000001 meters per second |

##### Acceleration

Metric Unit | Equivalent in SI Base Units |
---|---|

Meter per second squared (m/s²) | 1 meter per second squared |

Centimeter per second squared (cm/s²) | 0.01 meters per second squared |

Millimeter per second squared (mm/s²) | 0.001 meters per second squared |

Micrometer per second squared (µm/s²) | 0.000001 meters per second squared |

Nanometer per second squared (nm/s²) | 0.000000001 meters per second squared |

Picometer per second squared (pm/s²) | 0.000000000001 meters per second squared |

##### Force

Metric Unit | Equivalent in SI Base Units |
---|---|

Newton (N) | 1 kilogram meter per second squared |

Kilonewton (kN) | 1,000 newtons |

Hectonewton (hN) | 100 newtons |

Decanewton (daN) | 10 newtons |

Newton (N) | 1 newton |

Decinewton (dN) | 0.1 newtons |

Centi | 0.01 newtons |

##### Imperial vs Metric System

The imperial system and the metric system are two different systems of measurement. The imperial system is based on the English system of measurement, while the metric system is based on the decimal system.

##### History

The imperial system has been used in the United States since the 18th century. It is still used in the United States today, although the metric system is becoming more common. The metric system was developed in France in the 18th century. It is now the most widely used system of measurement in the world.

##### Units of Measurement

The imperial system and the metric system use different units of measurement. Some of the most common units of measurement in the imperial system include:

- Inches
- Feet
- Yards
- Miles
- Pounds
- Ounces
- Gallons

Some of the most common units of measurement in the metric system include:

- Millimeters
- Centimeters
- Meters
- Kilometers
- Grams
- Kilograms
- Liters

##### Conversion Factors

There are conversion factors that can be used to convert between the imperial system and the metric system. Some of the most common conversion factors include:

- 1 inch = 2.54 centimeters
- 1 foot = 0.3048 meters
- 1 yard = 0.9144 meters
- 1 mile = 1.6093 kilometers
- 1 pound = 0.4536 kilograms
- 1 ounce = 28.35 grams
- 1 gallon = 3.7854 liters

##### Advantages and Disadvantages

The imperial system and the metric system both have advantages and disadvantages. Some of the advantages of the imperial system include:

- It is familiar to people in the United States.
- It is easy to use for everyday measurements.

Some of the disadvantages of the imperial system include:

- It is not as precise as the metric system.
- It is not as widely used as the metric system.

Some of the advantages of the metric system include:

- It is more precise than the imperial system.
- It is more widely used than the imperial system.
- It is easier to convert between different units of measurement.

Some of the disadvantages of the metric system include:

- It is not as familiar to people in the United States.
- It can be difficult to use for everyday measurements.

The imperial system and the metric system are two different systems of measurement. The imperial system is still used in the United States today, although the metric system is becoming more common. The metric system is the most widely used system of measurement in the world.

##### Applications of Metric System

The metric system is an international system of units that is based on the decimal system. It is the most widely used system of measurement in the world, and it is used in almost every country except the United States.

The metric system has many advantages over other systems of measurement. It is easy to use, it is consistent, and it is precise. The metric system is also based on natural units, such as the meter and the kilogram, which makes it easy to understand and use.

##### Some of the applications of the metric system include:

**Science and engineering:**The metric system is the standard system of measurement used in science and engineering. It is used to measure everything from the smallest atoms to the largest galaxies.**Medicine:**The metric system is used to measure everything from body temperature to blood pressure. It is also used to measure the dosage of medications.**Manufacturing:**The metric system is used to measure everything from the size of screws to the weight of cars. It is also used to measure the accuracy of machines.**Transportation:**The metric system is used to measure everything from the speed of cars to the distance between cities. It is also used to measure the amount of fuel that vehicles use.**Trade:**The metric system is used to measure everything from the weight of food to the volume of oil. It is also used to measure the value of goods.

The metric system is a valuable tool that is used in many different fields. It is a system that is easy to use, consistent, and precise. The metric system is also based on natural units, which makes it easy to understand and use.

##### Benefits of the Metric System

There are many benefits to using the metric system, including:

**Simplicity:**The metric system is based on the decimal system, which makes it easy to understand and use.**Consistency:**The metric system is consistent throughout the world, which makes it easy to compare measurements from different countries.**Precision:**The metric system is very precise, which makes it ideal for use in science and engineering.**Universality:**The metric system is the most widely used system of measurement in the world, which makes it easy to communicate with people from other countries.

The metric system is a valuable tool that is used in many different fields. It is a system that is easy to use, consistent, precise, and universal. The metric system is the best system of measurement for the modern world.

##### Solved Examples of Metric System

The metric system is a decimal system of measurement that is based on the meter, kilogram, and second. It is the most widely used system of measurement in the world.

##### Example 1: Converting Meters to Kilometers

**A marathon is 42 kilometers long. How many meters is this?**

To convert kilometers to meters, multiply the number of kilometers by 1000.

42 km × 1000 m/km = 42,000 m

Therefore, a marathon is 42,000 meters long.

##### Example 2: Converting Grams to Kilograms

**A bag of sugar weighs 1 kilogram. How many grams is this?**

To convert kilograms to grams, multiply the number of kilograms by 1000.

1 kg × 1000 g/kg = 1000 g

Therefore, a bag of sugar weighs 1000 grams.

##### Example 3: Converting Liters to Milliliters

**A bottle of water contains 1 liter of water. How many milliliters is this?**

To convert liters to milliliters, multiply the number of liters by 1000.

1 L × 1000 mL/L = 1000 mL

Therefore, a bottle of water contains 1000 milliliters of water.

##### Example 4: Converting Celsius to Fahrenheit

**The temperature outside is 25 degrees Celsius. What is this temperature in Fahrenheit?**

To convert Celsius to Fahrenheit, multiply the temperature in Celsius by 9/5 and then add 32.

25°C × 9/5 + 32 = 77°F

Therefore, the temperature outside is 77 degrees Fahrenheit.

##### Example 5: Converting Fahrenheit to Celsius

**The temperature outside is 98.6 degrees Fahrenheit. What is this temperature in Celsius?**

To convert Fahrenheit to Celsius, subtract 32 from the temperature in Fahrenheit and then multiply the result by 5/9.

98.6°F - 32 = 66.6°C

66.6°C × 5/9 = 37°C

Therefore, the temperature outside is 37 degrees Celsius.