## Table of Contents

- Metric System: Background
- Metric System Units
- Understanding Metric Measurements
- Metric System Conversion
- Lesson Summary

Learn about the metric measurements and the metric system units . See how metric system conversion works and compare the measurements to English system.
Updated: 11/03/2021

- Metric System: Background
- Metric System Units
- Understanding Metric Measurements
- Metric System Conversion
- Lesson Summary

The** International System of Units** (abbreviated as SI from the French *Systeme International d'unites*) is the international standard system of measurement. It is commonly known as the **metric system**, originally developed in France in the late 18th century.

The metric system is based on a factor of 10 or a decimalized system. **Prefixes** are used to differentiate small from large units. Listed in the table below are the common prefixes used.

Prefix | Abbreviation | Value | Prefix | Abbreviation | Value |
---|---|---|---|---|---|

yotta | Y | 10^{24} |
deci | d | 10^{-1} |

zetta | Z | 10^{21} |
centi | c | 10^{-2} |

exa | E | 10^{18} |
milli | m | 10^{-3} |

peta | P | 10^{15} |
micro | Greek letter mu | 10^{-6} |

tera | T | 10^{12} |
nano | n | 10^{-9} |

giga | G | 10^{9} |
pico | p | 10^{-12} |

mega | M | 10^{6} |
femto | f | 10^{-15} |

kilo | k | 10^{3} |
atto | a | 10^{-18} |

hecto | h | 10^{2} |
zepto | z | 10^{-21} |

deka | da | 10^{1} |
yocto | y | 10^{-24} |

The base 10 system of the metric system explains why it is easier to convert from one unit to another. Its base units are in line with defining constants rather than artifacts and material properties, making it possible to reproduce it anywhere accurately. It has been widely used in science and engineering because the common set of standard units makes it easier for scientists and engineers to replicate and review results from other studies.

Different metric system units can be presented along with some common units from the English system of measurement for comparison. The metric system is already standardized and used in most places, while the English system is commonly used in the United States. The metric system only requires using the factors of 10 to convert, while the English system needs a conversion ratio to convert accurately from one unit to another.

**Base units ** comprise all the other units known today. Each base unit is defined by a standard defining constant. What are the base units of the metric system? Refer to the table provided below.

Base Unit | Quantity | Symbol |
---|---|---|

second | time | s |

meter | length | m |

kilogram | mass | kg |

ampere | electric current | A |

kelvin | thermodynamic temperature | K |

mole | amount of substance | mol |

candela | luminous intensity | cd |

Derived units are combinations of the base units. For example, area refers to the space occupied by a two-dimensional region. It is a product of two lengths; thus, its unit is m{eq}^2 {/eq}. Other examples of derived units are speed (m/s), density (kg/m{eq}^3 {/eq}), and volume (m{eq}^3 {/eq}).

Some of the common metric measurements encountered every day are length, mass, volume, density, and temperature. There are different units used to express these quantities.

**Length** is a measure of distance. Its SI unit is the **meter (m)**. As a base unit, its technical definition is related to the speed of light in a vacuum at 299 792 458 m/s.

Small distances use prefixes, such as centi- (10{eq}^{-2} {/eq}) and milli- (10{eq}^{-3} {/eq}). In this instance, 1 cm is equal to 0.01 m, and 1 mm is equal to 0.001 m. Common prefixes used for large distances are kilo- (10{eq}^{3} {/eq}) and mega- (10{eq}^{6} {/eq}). A distance of 1 km is equivalent to 1000 m, while 1 Mm is 1 000 000 m.

The basic units of length in the English system are inch, foot, and mile. These units are now defined in terms of meter. One inch (in.) is defined exactly as 2.54 cm, and 1 cm = 0.01 m. Using this definition, one can also easily convert other units to meters. Some of the unit conversions used in the English system are:

- 12 in = 1 ft
- 3 ft = 1 yd
- 5280 ft = 1 mi
- 1760 yd = 1 mi

**Mass** refers to the amount of matter an object contains. Its SI unit equivalent is the **kilogram (kg)**. The previous definition of the kilogram is based on the mass of a platinum-iridium cylinder, but it gradually loses some of its mass, leading to the creation of a more definite and unchanging standard. Today, its definition is tied to the fixed value of the Planck constant at 6.626 070 15 {eq}\times {/eq} 10{eq}^{-34} {/eq} J s.

Among the base units, only the kilogram has a prefix on it. One kilogram is equal to 1000 g. Similar to length, prefixes such as milli- (10{eq}^{-3} {/eq}) for small objects and kilo- (10{eq}^3 {/eq}) for heavier objects express mass in SI units.

The most common units of mass (or weight) in the English system are ounce (oz), pound (lb), and ton. These units are related to the kilogram using the conversion 1 kg {eq}\approx {/eq} 2.205 lb. The conversion ratios of these English units are:

- 16 oz = 1 lb
- 2000 lb = 1 ton

Mass and weight are two different quantities. **Mass** is the amount of matter contained in an object, while **weight** measures the amount of gravitational force exerted on an object. Mass remains constant regardless of location, while weight is dependent on an object's location.

**Volume** refers to the amount of three-dimensional space occupied or enclosed by an object. It is calculated by multiplying the length, width, and height of an object. It is a product of three lengths, making its derived SI unit as **cubic meter** or m{eq}^3 {/eq}.

Small and large volumes in the metric system are indicated using prefixes. One cubic meter, for example, is equal to 1 000 000 000 mm{eq}^3 {/eq} and 1 000 000 cm{eq}^3 {/eq}. Since these units are not that convenient to use in liquids, the unit liter (L) is used even if it is not an official SI unit. One liter is a special name for a cubic decimeter (dm{eq}^3 {/eq}) and is also equal to 1000 cm{eq}^3 {/eq}. A smaller unit of volume is the milliliter (mL), so 1000 mL = 1 L.

Volumes of solids in the English system are given in cubic feet and cubic yards. The equivalent of these units and other common units of volume of fluids such as fluid ounce (oz), cup (c), pint (pt), quart (qt), gallon (gal) are listed below:

- 1 ft{eq}^3 {/eq} = 1728 in{eq}^3 {/eq}

- 1 yd{eq}^3 {/eq} = 27 ft{eq}^3 {/eq}

- 2 cup = 1 pt
- 32 oz = 1 qt
- 2 pt = 1 qt
- 4 qt = 1 gal

**Density** quantifies the degree of compactness of an object and helps determine whether an object will float or sink in water. It is also defined as the mass per unit volume, making it a derived unit. Since the SI unit of mass is kg and the standard unit of volume is m{eq}^3 {/eq}, the SI unit of density is {eq}\frac{kg}{m^3} {/eq}. Other units of density are g/mL and g/cm{eq}^3 {/eq}.

The relationship between the density, mass, and volume is given by {eq}\rho = \frac{m}{V} {/eq}, where {eq}\rho {/eq} is the density, *m* is the mass, and *V* is the volume. If the two quantities are given, then one can easily determine the one unknown quantity. Consider this example: Calculate the density of a wooden block with a mass of 15 g and a volume of 20 cm{eq}^3 {/eq}. Substitute the values for mass and volume in the equation for density, as shown:

{eq}\rho = \frac{m}{V}=\frac{15 g}{20 cm^3} = 0.75 \frac{g}{cm^3} {/eq}.

To determine whether an object will float or sink in water, compare its density with the density of water ({eq}\rho {/eq} = 1 g/cm{eq}^3 {/eq} or 1000 kg/m{eq}^3 {/eq}). If its density is greater than the density of water, it will sink. If it is less than the density of water, it will float. In the case of the wooden block, 0.75 g/cm{eq}^3 {/eq} < 1 g/cm{eq}^3 {/eq}, thus it will float.

**Temperature** is the quantity that describes the hotness and coldness of an object. It is the average kinetic energy of the molecules comprising the substance or object. Its SI unit is the **kelvin (K)**, defined based on the fixed value of the Boltzmann constant, k, equal to 1. 380 649 {eq}\times {/eq} 10{eq}^{-23} {/eq} J/K.

Aside from the Kelvin scale, the other two most common temperature scales are the Fahrenheit and the Celsius scales. The temperature can be converted from one unit to another using the equations below.

To convert Celsius to Fahrenheit and vice versa, use:

{eq}T_{^{\circ}C}=\frac{5}{9} (T_{^{\circ}F}-32) {/eq}

{eq}T_{^{\circ}F}=\frac{9}{5}T_{^{\circ}C}+32 {/eq}

To convert kelvin to Celsius and vice versa:

{eq}T_{^{\circ}C}=T_K -273.15 {/eq}

{eq}T_K=T_{^{\circ}C}+273.15 {/eq}

In converting Fahrenheit to kelvin, convert the temperature first to Celsius before converting it to kelvin.

In any method of converting units, whether from large to small, small to large, English to metric system conversion or vice versa, the table of prefixes and the conversions given in the previous sections are valuable tools. A ratio or a fraction, called **conversion factor**, is always equal to 1 and shows the relationship between units used in unit conversion. Ensure that the unit that needs to be removed is in the denominator for it to be canceled, while the desired unit is placed in the numerator.

Consider the examples below in converting larger to smaller units.

1. Use 1 km = 1000 m and 1 m = 100 cm.

Convert first the km to m before converting it to cm.

{eq}55 \text{ km} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{100 \text{ cm}}{1 \text{ m}} = 5.50\times 10^{6} \text{ cm} {/eq}.

2. Convert 20 {eq}^3 {/eq} to mm{eq}^3 {/eq}. Use the conversion factor 1 m = 1000 mm. Ensure that the conversion factors are also raised to three.

{eq}20 \text{ m}^3 \times (\frac{1000 \text{ mm}}{1 \text{ m}})^3 = 2\times 10^{10} \text{ mm}^3 {/eq}

3. Convert 25 ton to g.

Use the following conversion factors: 2000 lb = 1 ton, 1 kg = 2.205 lb, 1 kg = 1000 g.

{eq}25 \text{ ton} \times \frac{2000 \text{ lb}}{1 \text{ ton}} \times \frac{1 \text{ kg}}{2.205 \text{ lb}} \times \frac{1000 \text{ g}}{1 \text{ kg}} =2.268\times 10^7 \text{ g} {/eq}

The same method applies when converting smaller to larger units. Consider the examples below.

1. Convert 1500 cm to km.

{eq}1500 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} \times \frac{1 \text{ km}}{1000 \text{ m}} = 0.015 \text{ km} {/eq}

2. Convert 4.25 {eq}\times {/eq} 10{eq}^9 {/eq} mm{eq}^3 {/eq} to m{eq}^3 {/eq}.

{eq}(4.25\times 10^9 \text{ mm}^3) \times (\frac{1 \text{ m}}{1000 \text{ mm}})^3 = 4.25 \text { m}^3 {/eq}

3. Convert 1 ton to g.

{eq}1 \text{ ton} \times \frac{2000 \text{ lb}}{1 \text{ ton}} \times \frac{1 \text{ kg}}{2.205 \text{ lb}} \times \frac{1000 \text{ g}}{1 \text{ kg}} = 907 029 \text { g} {/eq}

The **International System of Units** (SI), commonly known as the metric system, is the standard system of measurement. It is based on a factor of 10 or a decimalized system. Prefixes are used to differentiate large from small numbers. Physical quantities such as length, mass, volume, density, and temperature have the following corresponding SI units: length in meter; mass in kilogram; volume in m{eq}^3 {/eq}; density in kg/m{eq}^3 {/eq}; and temperature in kelvin. Some of the English system units are also defined in terms of the metric system.

A conversion factor is needed to convert from one unit to another. In using the conversion factor, the unit that needs to be removed should be placed in the denominator, while the desired unit should be in the numerator to ensure that the units will be properly canceled.

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- Activities
- FAQs

In this activity, students will be practicing measuring different quantities using the metric system and converting between units. For example, students might measure the length of their desk in meters, then convert it to kilometers. Students will choose at least one object for each quantity discussed in the lesson. To do this activity, you'll need a meter stick, a scale to measure mass, and a thermometer that can measure in Celsius. If you only have a ruler or a Fahrenheit thermometer, you can use a simple internet search to help you convert these values into the metric system. Then, let students convert within the metric system on their own.

In this activity, you're going to be measuring different objects around you and converting the measurements with the metric system. You should choose one object for each category and initially measure it using the units indicated in the table below. Then, convert it to the other units explained in the lesson. The first row has been filled in as an example. Once you're finished, answer the analysis questions below.

Quantities | Object | Initial Measurement | Conversions |
---|---|---|---|

Length (Example) | Desk | 1m | 0.1km, 100cm, 1000mm |

Length | |||

Mass | |||

Volume | |||

Density | |||

Temperature |

- Which quantities were easier to measure and why?
- Why do you think the metric system is used all over the world?
- Why do you think that there are different units for each quantity in the metric system, such as meters and kilometers?

Students will probably find length the easiest to measure, since they are all familiar with this linear quantity. Things that students are less familiar with like density or volume might be more difficult. Students should recognize the ease of the metric system, since it is based on a numerical system of tens. Students should also notice that some units are better for measuring certain things. For example, it's easiest to measure a desk in meters, but a larger unit would be needed to measure the distance between cities.

Physical quantities such as length, mass, volume, density, and temperature have corresponding SI units. These are the following: length in m; mass in kg; volume in cubic meter; density in kilogram per cubic meter; and temperature in kelvin. Prefixes (i.e., centi-, centi-, and kilo-) are used to differentiate between small and large quantities.

The seven base units in the metric system (or the SI system) are the meter (m), the kilogram (kg), the second (s), the kelvin (K), the ampere (A), the mole (mol), and the candela (cd).

A conversion factor is used to convert metric units to English units. It is a ratio that shows the relationship between units and is always equal to 1. During conversion, ensure that the unit that needs to be canceled is in the denominator, while the desired unit is placed in the numerator.

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