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| A '''minute of arc''', '''arcminute''', or '''minute arc''' ('''MOA'''), is a unit of [[angle|angular measurement]] equal to one sixtieth ({{frac|1|60}}) of one [[Degree (angle)|degree]]. In turn, a '''second of arc''' or '''arcsecond''' is one sixtieth ({{frac|1|60}}) of one arcminute. Because one degree is defined as one three hundred and sixtieth ({{frac|1|360}}) of a rotation, one minute of arc is {{frac|1|21,600}} of a rotation, which also equals {{frac|π|10,800}} [[radian]]s. It is used in those fields that require a unit for the expression of small angles, such as [[astronomy]], [[optometry]], [[ophthalmology]], [[optics]], [[navigation]] and [[marksmanship]].
| | It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br><br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>Here's more information on [http://www.youtube.com/watch?v=90z1mmiwNS8 Dentists in DC] visit the internet site. |
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| The number of square arcminutes in a complete sphere is
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| : <math>4 \pi \left(\frac{1}{\pi}10\,800\right)^2 = \frac{1}{\pi}466\,560\,000,</math>
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| or approximately 148,510,660.498 square arcminutes.
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| The arcsecond is {{frac|1|3,600}} of a degree, or {{frac|1|1,296,000}} of a circle, or {{frac|π|648,000}} [[radian]]s (which is approximately {{frac|1|206,265}} [[radian]]).
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| To express even smaller angles, standard [[SI prefix]]es can be employed; in particular, the '''milliarcsecond''', abbreviated '''mas''', is used in [[astronomy]].
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| ==Symbols and abbreviations==
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| The standard symbol for marking the arcminute is the [[prime (symbol)|prime]] (′) (U+2032), though a single quote (') (U+0027) is commonly used where only [[ASCII]] characters are permitted. One arcminute is thus written 1′. It is also abbreviated as '''arcmin''' or '''amin''' or, less commonly, the prime with a [[circumflex]] over it (<math>\hat{'}</math>).
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| The standard symbol for the arcsecond is the [[double prime]] (″) (U+2033), though a double quote (") (U+0022) is commonly used where only [[ASCII]] characters are permitted. One arcsecond is thus written 1″. It is also abbreviated as '''arcsec''' or '''asec'''.
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| {|cellpadding=1 cellspacing=0 class="wikitable" style="margin: 0 auto"
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| |+ '''The [[sexagesimal]] system of [[Angle|angular measurement]]'''
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| ! scope="col" | Unit !! scope="col" | Value !! scope="col" | Symbol !! scope="col" | Abbreviations !! scope="col" | In radians (approx.)
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| ! scope="row" | [[degree (angle)|Degree]]
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| | {{frac|1|360}} circle || [[degree symbol|°]] || deg||align="right"|17.4532925 mrad
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| ! scope="row" | Arcminute
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| | {{frac|1|60}} degree || ′ ([[prime (symbol)|prime]]) || arcmin, amin, am, <math>\hat{'}</math>, MOA||align="right"|290.8882087 µrad
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| ! scope="row" | Arcsecond
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| | {{frac|1|60}} arcminute || ″ (double prime) || arcsec, asec, as||align="right"| 4.8481368 µrad
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| ! scope="row" | Milliarcsecond
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| | {{frac|1|1,000}} arcsecond || || mas||align="right"|4.8481368 nrad
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| ! scope="row" | Microarcsecond
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| | 10<sup>−6</sup> arcsecond || || μas||align="right"|4.8481368 prad
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| |}
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| In [[celestial navigation]], seconds of arc are rarely used in calculations, the preference usually being for degrees, minutes and decimals of a minute, written for example as 42° 25.32′ or 42° 25.322′.<ref>{{cite web|title=CELESTIAL NAVIGATION COURSE|url=http://www.learntonavigate.com/celestial.htm|publisher=International Navigation School|accessdate=4 November 2010|quote=It is a straight forward method [to obtain a position at sea] and requires no mathematical calculation beyond addition and subtraction of degrees and minutes and decimals of minutes}}</ref><ref>{{cite web|title=Astro Navigation Syllabus|url=http://www.kumquat-data.com/Astro%20Navigation%20Syllabus.htm|accessdate=4 November 2010|quote=[Sextant errors] are sometimes [given] in seconds of arc, which will need to be converted to decimal minutes when you include them in your calculation.}}</ref> This notation has been carried over into [[Global Positioning System|marine GPS]] receivers, which normally display latitude and longitude in the latter format by default.<ref>{{cite web|title=Shipmate GN30|url=http://norinco.co.in/NCMS/index.php?option=com_content&task=view&id=53&Itemid=81|publisher=Norinco|accessdate=4 November 2010}}</ref>
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| ==Uses==
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| ===Firearms===
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| The arcminute is commonly found in the [[firearm]]s industry and literature, particularly concerning the accuracy of [[rifle]]s, though the industry refers to it as '''minute of angle'''. It is especially popular with shooters familiar with the [[Imperial measurement system]] because 1 MOA [[subtend]]s approximately one [[inch]] at 100 [[yard]]s, a traditional distance on [[Shooting range|target ranges]]. Since most modern rifle scopes are adjustable in half ({{frac|1|2}}), quarter ({{frac|1|4}}), or eighth ({{frac|1|8}}) MOA increments, also known as ''clicks'', this makes zeroing and adjustments much easier. For example, if the point of impact is 3" high and 1.5" left of the point of aim at 100 yards, the scope needs to be adjusted 3 MOA down, and 1.5 MOA right. Such adjustments are trivial when the scope's adjustment dials have an MOA scale printed on them, and even figuring the right number of clicks is relatively easy on scopes that ''click'' in fractions of MOA.
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| One thing to be aware of is that some scopes, including some higher-end models, are calibrated such that an adjustment of 1 MOA corresponds to exactly 1 inch, rather than 1.047". This is commonly known as the Shooter's MOA (SMOA) or Inches Per Hundred Yards (IPHY). While the difference between one true MOA and one SMOA is less than half of an inch even at 1000 yards,<ref>http://www.shootingillustrated.com/index.php/6227/mil-moa-or-inches/</ref> this error compounds significantly on longer range shots that may require adjustment upwards of 20-30 MOA to compensate for the bullet drop. If a shot requires an adjustment of 20 MOA or more, the difference between true MOA and SMOA will add up to 1 inch or more. In competitive target shooting, this might mean the difference between a hit and a miss.
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| The physical group size equivalent to ''m'' minutes of arc can be calculated as follows: group size = tan({{frac|''m''|60}}) × distance. In the example previously given, for 1 minute of arc, and substituting 3,600 inches for 100 yards, 3,600 tan({{frac|1|60}}) = 1.047 inches. In [[metric units]] 1 MOA at 100 meters = 2.908 centimeters.
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| Sometimes, a precision firearm's accuracy will be measured in MOA. This simply means that under ideal conditions i.e. no wind, match-grade ammo, clean barrel, and a vise or a benchrest used to eliminate shooter error, the gun is capable of producing a group of shots whose center points (center-to-center) fit into a circle, the average diameter of circles in several groups can be subtended by that amount of arc. For example, a ''1 MOA rifle'' should be capable, under ideal conditions, of shooting an average 1-inch groups at 100 yards. Most higher-end rifles are warrantied by their manufacturer to shoot under a given MOA threshold (typically 1 MOA or better) with specific ammunition and no error on the shooter's part. For example, Remington's [[M24 Sniper Weapon System]] is required to shoot 0.8 MOA or better, or be rejected.
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| Rifle manufacturers and gun magazines often refer to this capability as ''sub-MOA'', meaning it shoots under 1 MOA. This means that a single group of 3 to 5 shots at 100 yards, or the average of several groups, will measure less than 1 MOA between the two furthest shots in the group, i.e. all shots fall within 1 MOA. If larger samples are taken (i.e., more shots per group) then group size typically increases, however this will ultimately average out. If a rifle was truly a 1 MOA rifle, it would be just as likely that two consecutive shots land exactly on top of each other as that they land 1 MOA apart. For 5 shot groups, based on 95% confidence a rifle that normally shoots 1 MOA can be expected to shoot groups between 0.58 MOA and 1.47 MOA, although the majority of these groups will be under 1 MOA. What this means in practice is if a rifle that shoots 1" groups on average at 100 yards shoots a group measuring .7" followed by a group that is 1.3" this is not statistically abnormal.<ref>{{cite web |first=Robert E. |last=Wheeler |date= |title=Statistical notes on rifle group patterns |url=http://www.bobwheeler.com/guns/GroupStat.pdf |accessdate=21 May 2009}}</ref><ref>{{cite journal |unused_data=mdy |first=Denton |last=Bramwell |date=January 2009 |title=Group Therapy The Problem: How accurate is your rifle? |url=http://www.longrangehunting.com/articles/accurate-rifle-groups-1.php |journal=Varmint Hunter |volume=69 |accessdate=21 May 2009}}</ref>
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| The [[Metric system|Metric System]] counterpart of the MOA is the '''MilRad''', being equal to one 1000th of the target range, laid out on a circle that has the observer as centre and the target range as radius. The number of MilRads on a full such circle therefore always is equal to 2 x π x 1000, regardless the target range. Therefore 1 MOA = 0.2908 MilRad. This means that an object which spans 1 MilRad on the [[reticle]] is at a range that is in meters equal to the object's size in millimeters (e.g. an object of 100 mm @ 1 Milrad is 100 meters away). So there is no conversion factor required, contrary to the MOA system. The markings on a reticle that mark MilRads are called '''MilDots'''. Such reticle is called a ''MilDot Reticle''.
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| ===Cartography===
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| Minutes of arc (and its subunit, seconds of arc or SOA—equal to a sixtieth of a MOA) are also used in [[cartography]] and [[navigation]]. At [[sea level]] one minute of arc along the [[equator]] or a [[Meridian (geography)|meridian]] equals approximately one [[Nautical mile]] ({{convert|1.852|km|mi|disp=or|abbr=on}}). A second of arc, one sixtieth of this amount, is about 30 meters or roughly 100 feet. The exact distance varies along meridians because the [[geoid|shape of the Earth]] is slightly [[Oblate spheroid|oblate]].
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| Positions are traditionally given using degrees, minutes, and seconds of arcs for [[latitude]], the arc north or south of the equator, and for [[longitude]], the arc east or west of the [[Prime Meridian]]. Any position on or above the Earth's [[reference ellipsoid]] can be precisely given with this method. However, because of the somewhat clumsy [[radix|base]]-60 nature of minutes and seconds, positions are frequently expressed in fractional degrees only, expressed in decimal form to an equal amount of precision. Degrees given to three decimal places ({{frac|1|1,000}} of a degree) have about {{frac|1|4}} the precision of degrees-minutes-seconds ({{frac|1|3,600}} of a degree) and specify locations within about 120 meters or 400 feet.
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| ===Property cadastral surveying===
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| Related to cartography, property boundary [[surveying]] using the [[metes and bounds]] system relies on fractions of a degree to describe property lines' angles in reference to [[cardinal direction]]s. A boundary "mete" is described with a beginning reference point, the cardinal direction North or South followed by an angle less than 90 degrees and a second cardinal direction, and a linear distance. The boundary runs the specified linear distance from the beginning point, the direction of the distance being determined by rotating the first cardinal direction the specified angle toward the second cardinal direction. For example, ''North 65° 39′ 18″ West 85.69 feet'' would describe a line running from the starting point 85.69 feet in a direction 65° 39′ 18″ (or 65.655°) away from north toward the west.
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| ===Astronomy===
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| [[File:Comparison angular diameter solar system.svg|thumb|300px|Comparison of angular diameter of the Sun, Moon, planets and the International Space Station. To get a true representation of the sizes, view the image at a distance of 103 times the width of the "Moon: max." circle. For example, if this circle is 10 cm wide on your monitor, view it from 10.3 m away.]]
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| The arcminute and arcsecond are also used in [[astronomy]]. Degrees (and therefore arcminutes) are used to measure [[declination]], or angular distance north or south of the [[celestial equator]]. The arcsecond is also often used to describe [[parallax]], due to very small parallax angles for [[stellar parallax]], and tiny angular diameters (e.g., Venus varies between 10′′ and 60′′). The parallax, [[proper motion]] and angular diameter of a star may also be written in milliarcseconds (mas), or thousandths of an arcsecond. The [[parsec]] gets its name from "parallax second", for those arcseconds.
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| The ESA [[astrometry|astrometric]] space probe [[Gaia mission|Gaia]] is hoped to measure star positions to 20 microarcseconds (µas) when it begins producing catalog positions sometime after 2016. There are about 1.3 trillion µas in a circle. As seen from Earth, one µas is about the size of a period at the end of a sentence in the Apollo mission manuals left on the moon. Currently the best catalog positions of stars actually measured are in terms of milliarcseconds, by the [[U.S. Naval Observatory]]. A milliarcsecond is about the size of a dime atop the Eiffel Tower as seen from New York City.
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| Apart from the Sun, the star with the largest [[angular diameter]] from Earth is [[R Doradus]], a red [[supergiant]] with a diameter of 0.05 arcsecond.<ref>Some studies have shown a larger angular diameter for [[Betelgeuse]]. Various studies have produced figures of between 0.042 and 0.069 arcseconds for the star's diameter. The variability of Betelgeuse and difficulties in producing a precise reading for its angular diameter make any definitive figure conjectural.</ref> Because of the effects of atmospheric [[astronomical seeing|seeing]], ground-based [[telescope]]s will smear the image of a star to an angular diameter of about 0.5 arcsecond; in poor seeing conditions this increases to 1.5 arcseconds or even more. The dwarf planet [[Pluto]] has proven difficult to resolve because its [[angular diameter]] is about 0.1 arcsecond.<ref>[http://nssdc.gsfc.nasa.gov/planetary/factsheet/plutofact.html NASA.gov] Pluto Fact Sheet</ref> This is roughly equivalent to a (40 mm) [[Table tennis|ping-pong]] ball viewed at a distance of 50 miles (80 km).
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| Space telescopes are not affected by the Earth's atmosphere but are [[Diffraction limit#Diffraction limit of telescopes|diffraction limited]]. For example, the [[Hubble space telescope]] can reach an angular size of stars down to about 0.1″. Techniques exist for improving seeing on the ground. [[Adaptive optics]], for example, can produce images around 0.05 arcsecond on a 10 m class telescope.
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| ===Human vision===
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| In humans, [[Visual acuity#Normal vision|20/20 vision]] is the ability to resolve a [[spatial pattern]] separated by a [[visual angle]] of one minute of arc.
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| A 20/20 letter subtends 5 minutes of arc total.
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| ===Materials===
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| The deviation from parallelism between two surfaces, for instance in [[optical engineering]], is usually measured in arcminutes or arcseconds.
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| == Notes and references ==
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| {{Reflist|2}}
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| == External links ==
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| * [http://www.scribd.com/doc/2068496/Mils-and-MOA-A-Tactical-Shooters-Guide MOA: Rifle Reticles] by Robert Simeone
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| {{SI units}}
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| {{Use dmy dates|date=August 2010}}
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| [[Category:Units of angle|Arcminute]]
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It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.
Here are some common dental emergencies:
Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.
At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.
Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.
Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.
Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.
Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.
Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.
In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.
Here's more information on Dentists in DC visit the internet site.