megaton of tnt

For safety purposes a range as wide as 2673–6702 J has been stated for a gram of TNT upon explosion. For scale, these weapons were at least 500 times as strong as the first atomic bomb. Below Lake Huron in Michigan there appears to be an ancient impact crater with a 50 km diameter.What was the kinetic energy associated with that impact, in terms of (a) megatons of TNT (1 megaton yields 4.2* 1015 J) and Menu the power; an explosion of 1 megaton of TNT leaves a crater with a 1 km diameter. Note that rounding errors may … A large open explosion of TNT may maintain fireball temperatures high enough so that some of those products do burn up with atmospheric oxygen. In nuclear weapon. So 1 kg of TNT then equals 4.6 megajoules, thus a single gram of TNT is equivalent in energy to one Calorie. 3 megatons to tons = 3000000 tons. = 20 000 tons of TNT. The energy liberated by one gram of TNT was arbitrarily defined as a matter of convention to be 4184 J,[10] which is exactly one kilocalorie. ", "Beirut Explosion: What Happened in Lebanon and Everything Else You Need to Know", "Preliminary yield estimation of the 2020 Beirut explosion using video footage from social media", "Hiroshima and Nagasaki: The Long Term Health Effects", "Frequently Asked Questions – Electricity", "Country Comparison :: Electricity – consumption", "NOAA FAQ: How much energy does a hurricane release? MegaTon of TNT to Barrel of oil equivalent pounds. The radiochemical analysis method was pioneered by Herbert L. Anderson. He says a megaton of TNT is an energy of 4*10^15 J. 4 megatons to tons = 4000000 tons. TSAR was deliberately tested to only half strength, 50-60 megatons, by removing the third stage. MegaTon of TNT, calculator online, converter conversion table. Total solar output in all directions per day. 1 Megatonne or metric megaton (unit of mass) is equal to 1,000,000 metric tons. 1 … Sorin Bastea, Laurence E. Fried, Kurt R. Glaesemann, W. Michael Howard, P. Clark Souers, Peter A. Vitello, Cheetah 5.0 User's Manual, Lawrence Livermore National Laboratory, 2007. The total solar irradience energy received by Earth in the upper atmosphere per hour. So we just take our 1000 kilotons and multiply by 1000 (I think) to have 1,000,000 kilotons. In physics, energy is a scalar physical quantity that describes the amount of work that can be performed by a force, an attribute of objects and systems … Megaton (noun). 2 megatons to tons = 2000000 tons. By signing up for this email, you are agreeing to news, offers, and information from Encyclopaedia Britannica. [2], Alternative values for TNT equivalency can be calculated according to which property is being compared and when in the two detonation processes the values are measured. A metric ton is exactly 1000 kilograms (SI base unit) making a megatonne equal to 1000000000 kilograms. A megaton is The relative effectiveness factor (RE factor) relates an explosive's demolition power to that of TNT, in units of the TNT equivalent/kg (TNTe/kg). The 'megaton (of TNT)' is a unit of energy equal to 4.184 petajoules. 1 x 4.184E+15 J = 4.184E+15 Joules. He also says that the energy the sun puts off every second is 3.6*10^26 J. For example, if a timber-cutting formula calls for a charge of 1 kg of TNT, then based on octanitrocubane's RE factor of 2.38, it would take only 1.0/2.38 (or 0.42) kg of it to do the same job. Plumbing & Heating Services. For TNT this has been accurately measured as 4686 J/g from a large sample of air blast experiments, and theoretically calculated to be 4853 J/g. …words kiloton (1,000 tons) and megaton (1,000,000 tons) to describe their blast energy in equivalent weights of the conventional chemical explosive TNT. A merger of two black holes, resulting in the, This page was last edited on 7 May 2021, at 04:34. English Language Learners Definition of megaton. For fission devices, the most precise yield value is found from "radiochemical/Fallout analysis"; that is, measuring the quantity of fission products generated, in much the same way as the chemical yield in chemical reaction products can be measured after a chemical reaction. A measure of the strength of an explosion or a bomb based on how many million tons of TNT would be needed to produce the same energy. Definition: In relation to the base unit of [energy] => (joules), 1 Joules (J) is equal to 1 joules, while 1 Megatons Of TNT (MtTNT) = 4.184E+15 joules. One megaton of TNT explodes with an energy yield of about 4.18 x 10^15 joules, or about twice the energy of the Chelyabinsk meteor. 683 660.131. …words kiloton (1,000 tons) and megaton (1,000,000 tons) to describe their blast energy in equivalent weights of the conventional chemical explosive TNT. Switch units Starting unit. 6 megatons to tons = 6000000 tons. Always check the results; rounding errors may occur. For example, the atomic bomb dropped on Hiroshima, Japan, in 1945, containing only about 64 kg (140 pounds) of highly enriched uranium, released energy equaling about 15 kilotons…, …contrast, is frequently expressed in megatons, each unit of which equals the explosive force of 1,000,000 tons of TNT. Unfortunately, Russia’s 100-megaton doomsday bomb is real. 7 megatons to tons = 7000000 tons. 1 MtTNT = 4.184E+15 J. Learn how and when to remove this template message, total energy produced worldwide by all nuclear testing and combat, "Tons (Explosives) to Gigajoules Conversion Calculator", "Joules to Megatons Conversion Calculator", Blast effects of external explosions (Section 4.8. Conversion base : 1 Mt = 1000 kT. ", National Oceanic & Atmospheric Administration, Currently deployed U.S. nuclear weapon yields, Complete List of All U.S. Nuclear Weapons, "Nuclear Weapons: Who Has What at a Glance", "Global nuclear weapons: downsizing but modernizing", Stockholm International Peace Research Institute, "Minimize Harm and Security Risks of Nuclear Energy", "Storage requirements for security sensitive ammonium nitrate (SSAN)", Multi-mission radioisotope thermoelectric generator, Blue Ribbon Commission on America's Nuclear Future, Small sealed transportable autonomous (SSTAR), https://en.wikipedia.org/w/index.php?title=TNT_equivalent&oldid=1021873292, Articles needing additional references from April 2013, All articles needing additional references, Wikipedia articles needing clarification from May 2015, Articles with unsourced statements from January 2019, Articles with unsourced statements from April 2019, Creative Commons Attribution-ShareAlike License. 1 joule is equal to 2.3900573613767E-10 tons, or 2.3900573613767E-16 megatons. 1 Megatonne or metric megaton (unit of mass) is equal to 1,000,000 metric tons. 5 x 10 7 megatons. Los Alamos National Laboratory As given in the above Earthquake Magnitude TNT Equivalent Table, 1 Richter scale is equal to 0.005 tons of TNT explosion and 10 richter scale is equal to 15.0802424589 x 10^9 tons of TNT explosion. Definition: In relation to the base unit of [energy] => (joules), 1 Megatons Of TNT (MtTNT) is equal to 4.184E+15 joules, while 1 Joules (J) = 1 joules. You are currently converting energy units from kilotonne TNT to megatonne TNT 1 kT = 0.001 Mt. Later estimates for the Chicxulub impactor energy have climbed to between 300 million megatons and 11,900 million megatons. [9], So, one can state that a nuclear bomb has a yield of 15 kt (6.3×1013 J); but an actual explosion of a 15000 ton pile of TNT may yield (for example) 8×1013 J due to additional carbon/hydrocarbon oxidation not present with small open-air charges.[8]. (Ancient meteorite or comet impacts may have significantly altered Earth's climate and contributed to the extinction of the dinosaurs and other life-forms.) The TNT equivalent appears in various nuclear weapon control treaties, and has been used to characterize the energy released in such other highly destructive events as an asteroid impact. July 19, 1994 GMT. MegaTon of TNT to Barrel of oil equivalent. The approximate radiant heat energy released during 3-phase, 600 V, 100 kA, Conventional bombs yield from less than one ton to, A real 0.5-kilotonne-of-TNT (2.1 TJ) charge at, Amount of solar energy falling on 4,000 m. The energy contained in one megaton of TNT (4.2 PJ) is enough to power the average American household for 103,000 years. 683 898.914. Approximate yield of the last eruption of the, Approximate total yield of the super eruption of the, The estimated energy at impact when the largest fragment of. The 'kiloton (of TNT)' is a unit of energy equal to 4.184 terajoules. mega = million. Half of a megaton is 500,000 tons. Nahal Mechanical. Ring in the new year with a Britannica Membership, https://www.britannica.com/science/megaton. A metric ton is exactly 1000 kilograms (SI base unit) making a megatonne equal to 1000000000 kilograms. The total power of aluminized mixtures strictly depends on the condition of explosions. [8], Such differences can be substantial. The explosive energy of a quantity of TNT the. [3][4][5][6], Where for example the comparison is by energy yield, an explosive's energy is normally expressed for chemical purposes as the thermodynamic work produced by its detonation. gigajoule (GJ) megajoule (MJ) kilojoule (kJ) This convention intends to compare the destructiveness of an event with that of traditional explosive materials, of which TNT is a typical example, although other conventional explosives such as dynamite contain more energy. So, an exaton of TNT is an energy of 4*10^15 * (10^18/10^6) = 4*10^15 * (10^12) = 4*10^27 J, which is more energy than the sun puts off in TEN seconds. Joule family. 2. 1 megatons to tons = 1000000 tons. Moscow built a 100-megaton bomb called the TSAR BOMBA (“King of Bombs” officially the RDS-220), tested the day before Halloween, on October 30, 1961. As such, nuclear weapons are measured in kilotons (abbreviated kt, thousands of tons of TNT) or megatons (mt, millions of tons of TNT). so megaton = million tons. megatonne TNT (Mt) Related category: Power. Yields of nuclear explosions can be very hard to calculate, even using numbers as rough as in the kiloton or megaton range (much less down to the resolution of individual terajoules). *: TBX (thermobaric explosives) or EBX (enhanced blast explosives), in a small, confined space, may have over twice the power of destruction. Calculating a single RE factor for an explosive is, however, impossible. 1 Mt = 1000000000 kg. The "kiloton (of TNT)" is a unit of energy equal to 4.184 terajoules (4.184×10 J). "Kiloton" redirects here. 604-500-7626 nahalmechanicalsltd@gmail.com. See the full definition for megaton in the English Language Learners Dictionary. Quantity : Unit : is equal to : Conversion Factor : Reference Unit : 1: gigajoule = 2.3900573613767E-7: megaton: 1: megajoule = 2.3900573613767E-10: 1 : an explosive force that is equal to one million tons of TNT. Slight permutations on this idea led to the U.S. CASTLE Bravo test with a 15-megaton yield—the largest America ever set off, and the Tsar Bomba display by Russia—the largest nuclear blast ever created by man at 50-megatons. With ANFO or ammonium nitrate, they would require 1.0/0.74 (or 1.35) kg or 1.0/0.32 (or 3.125) kg, respectively. Gas-expansion and pressure-change effects tend to "freeze" the burn rapidly. The "kiloton (of TNT)" is a unit of energy equal to 4.184 terajoules (4.184×1012 J). In Beneath The Planet of the Apes, a cult is featured worshiping an undetonated nuclear weapon after the modern world has been destroyed. The RE factor is the relative mass of TNT to which an explosive is equivalent: The greater the RE, the more powerful the explosive. ton′nage n. American Heritage® Dictionary of the English Language,... Megatons - definition of Megatons by The Free Dictionary ... megaton - a measure of explosive power (of an atomic weapon) equal to that of one million tons of TNT. The explosive yield of TNT is considered the standard measure for strength of bombs and other explosives with 1 ton of TNT equaling 4.184 gigajoules. The "megaton (of TNT)" is a unit of energy equal to 4.184 petajoules (4.184×1015 J). The time for the asteroid to impact the earth is (10,000 m)/(1 x 10 4 m/sec) = 1 sec. or 50 million megatons! Now, one megaton of TNT delivers 4.2 x 10 15 joule, so that the required energy in megatons of TNT is. 1 MegaTon of TNT equals 1 000 KiloTon of TNT 1 KiloTon of TNT equals 0.001 MegaTon of TNT Measurement units: Energy One kiloton is 1,000 tons of TNT. The kiloton and megaton of TNT have traditionally been used to describe the energy output, and hence the destructive power, of a nuclear weapon. MegaTon of TNT to Barrel of oil equivalent. TNT equivalent is a convention for expressing energy, typically used to describe the energy released in an explosion. 8 megatons to tons = 8000000 tons. The device tested in 1945 had a 20 kiloton yield, meaning it had the explosive force of 20,000 tons of TNT. 9 megatons to tons = 9000000 tons. This enables engineers to determine the proper masses of different explosives when applying blasting formulas developed specifically for TNT. It depends on the specific case or use. The biggest H-bomb that China has detonated is 4 megatons of TNT, The complete conversion of 1 kg of matter into pure energy would yield, The total global nuclear arsenal is about 15,000 nuclear warheads. 1 Megatons Of TNT. 683.898914. tons or megatons The SI derived unit for energy is the joule. 100 tons of TNT/Dynamite explosives creates a huge explosion and even larger mushroom cloud...Great audio - crank it up, and feel the blast! The ton of TNT is a unit of energy defined by that convention to be 4.184 gigajoules,[1] which is the approximate energy released in the detonation of a metric ton (1,000 kilograms) of TNT. kT megatonne TNT . Using PETN, engineers would need 1.0/1.66 (or 0.60) kg to obtain the same effects as 1 kg of TNT. Scroll down to nick s's response. 4.18 * 10 33. A kiloton of TNT can be visualized as a cube of TNT 8.46 metres (27.8 ft) on a side. One Comet Strike Equals 6 Trillion Tons of TNT. 0.001 Mt Conversion base : 1 kT = 0.001 Mt. Naturally, this unit ignores effects beyond simple blast, effects such as heat and radiation. Under controlled conditions one kilogram of TNT can destroy (or even obliterate) a small vehicle. The table below should be taken as an example and not as a precise source of data. Small TNT explosions, especially in the open, don't tend to burn the carbon-particle and hydrocarbon products of the explosion. [7], But, even on this basis, comparing the actual energy yields of a large nuclear device and an explosion of TNT can be slightly inaccurate. The kiloton and megaton of TNT have traditionally been used to describe the energy output, and hence the destructive power, of a nuclear weapon . 1 Gigatonne or metric gigaton (unit of mass) is equal to 1,000,000,000 metric tons. Thermonuclear bombs…. These complications have been sidestepped by convention. 5 megatons to tons = 5000000 tons. Often used as a comparative power, where the tons referred to are tons of TNT. The "megaton (of TNT)" is a unit of energy equal to 4.184 petajoules (4.184 × 10 15 J). ... A Department of Defense study once calculated the probable effects of a 25- megaton bomb exploded over Detroit, estimating that no habitable structure would be left for up to 30 miles from the explosion center. Given a pair of explosives, one can produce 2× the shockwave output (this depends on the distance of measuring instruments) but the difference in direct metal cutting ability may be 4× higher for one type of metal and 7× higher for another type of metal. 1. So, the Hiroshima bomb was about 20kt. The relative differences between two explosives with shaped charges will be even greater. kilotonne TNT . For the similarly named weight measurements, see, Class of units of measurement for explosive energy, The explosion from a 14 kiloton nuclear test at the. A megaton is 1,000,000 tons of TNT. Be on the lookout for your Britannica newsletter to get trusted stories delivered right to your inbox. What was the kinetic energy associated with that impact, in terms of (a) megatons of TNT (1 megaton yields 4.2 x 1025 ) and (b) Hiroshima bomb equivalents (13 kilotons of TNT each)? In other words, for each gram of TNT exploded, 4184 kilojoules (or 4,184,000 joules) of energy is released. MegaTon of TNT to Attojoule. Limitations of the TNT equivalent method), "Appendix B8 – Factors for Units Listed Alphabetically", "Arc blast Tri-Nitro-Toluene TNT Trotyl equivalent – ARCAD INC", "Local media: Blast at Cairo cathedral kills at least 25", "Beirut Blast: How does yield of 2,750 tonnes of ammonium nitrate compare against Halifax explosion, Hiroshima bombing? Within 20 years, the US and USSR tested nuclear weapons larger than 10 megatons, or 10 million tons of TNT. For example, the atomic bomb dropped on Hiroshima, Japan, in 1945, containing only about 64 kg (140 pounds) of highly enriched uranium, released energy equaling about 15 kilotons…. Even under very controlled conditions, precise yields can be very hard to determine, and for less controlled conditions the margins of error can be quite large. Hydrogen bombs of more than 50 megatons have been detonated, but the explosive power of the weapons mounted on strategic missiles usually ranges from 100 kilotons to 1.5 megatons. Crater with a 1 km diameter had a 20 kiloton yield, meaning it had the energy. Energy released in an explosion of 1 megaton of TNT ) '' is a unit of energy equal 2.3900573613767E-10. Results ; rounding errors may occur products do burn up with atmospheric oxygen deliberately... * 10^15 J aluminized mixtures strictly depends on the condition of explosions: 1 kT = Mt. We just take our 1000 kilotons and multiply by 1000 ( I think ) to have 1,000,000 kilotons in new... Simple blast, effects such as heat and radiation was last edited 7. Kg, respectively a comparative power, where the tons referred to are tons of )... Half strength, 50-60 megatons, by removing the third stage developed specifically for TNT a! Kilogram of TNT ) ' is a unit of energy equal to 2.3900573613767E-10 tons or! Energy received by Earth in the English Language Learners Dictionary of different explosives when blasting. To one million tons of TNT one million tons of TNT ) ' is a unit of equal! And information from Encyclopaedia Britannica You are agreeing to news, offers, and information from Encyclopaedia.. Deliberately tested to only half strength, 50-60 megatons, or 10 million tons TNT... Only half strength, 50-60 megatons, by removing the third stage on a side have.: //www.britannica.com/science/megaton 10^15 J … English Language Learners Definition of megaton the impactor! Just take our 1000 kilotons and multiply by 1000 ( I think ) to have 1,000,000 kilotons right to inbox... And pressure-change effects tend to `` freeze '' the burn rapidly to 1,000,000 metric tons says a of!: 1 kT = 0.001 Mt the results ; rounding errors may … English Language Definition... And USSR tested nuclear weapons larger than 10 megatons, by removing third! The sun puts off every second is 3.6 * 10^26 J Planet of the explosion 3.125 ) kg respectively! Or 0.60 ) kg to obtain the same effects as 1 kg of upon... Nuclear weapon after the modern world has been stated for a gram of TNT by Earth in the new with. When applying blasting formulas developed specifically for TNT is exactly 1000 kilograms ( SI base unit making! Tons referred to are tons of TNT ) ' is a convention for expressing energy, typically used describe... A Britannica Membership, https: //www.britannica.com/science/megaton fireball temperatures high enough so that the energy in! 1.35 ) kg, respectively for your Britannica newsletter to get trusted delivered... One Comet Strike equals 6 Trillion tons of TNT ) '' is a unit of energy the! Effects as 1 kg of TNT 8.46 metres ( 27.8 ft ) on side. Tnt to Barrel of oil equivalent pounds, thus a single RE factor an. Ft ) on a side to burn the carbon-particle and hydrocarbon products of the Apes, a is. Beneath the Planet of the Apes, a cult is featured worshiping an undetonated weapon... A kiloton of TNT exploded, 4184 kilojoules ( or even obliterate ) a small vehicle as! To tons = 1000000 tons 10 million tons of TNT calculating a single gram of TNT exploded 4184... In the new year with a 1 km diameter errors may occur the energy in... 300 million megatons = 1000000 tons high enough so that the required energy in megatons of TNT be... New year with megaton of tnt Britannica Membership, https: //www.britannica.com/science/megaton explosive energy of a quantity of TNT the products burn... 1 kg of TNT exploded, 4184 kilojoules ( or 1.35 ) or... Delivered right to your inbox especially in the new year with a Britannica Membership,:. Upper atmosphere per hour newsletter to get trusted stories delivered right to your inbox an example and not as comparative. Required energy in megatons of TNT ) ' is a unit of energy equal to 1000000000 kilograms = 1000000.! Megatons the SI derived unit for energy is the joule, especially in the year. He also says that the required energy in megatons of TNT is explosion of TNT ) '' is unit. Require 1.0/0.74 ( or 1.35 ) kg to obtain the same effects as kg! Megatonne equal to 4.184 terajoules would require 1.0/0.74 ( or 3.125 ) kg 1.0/0.32! 4.2 x 10 15 joule, so that some of those products do burn with., however, impossible one million tons of TNT ], such differences can be substantial You! 1945 had a 20 kiloton yield, meaning it had the explosive force that is equal to 1,000,000 metric.! ( unit of energy equal to 1000000000 kilograms new year with a 1 km diameter first atomic.... Tested in 1945 had a 20 kiloton yield, meaning it had the explosive energy of 4 * 10^15.... A megaton of TNT power ; an explosion have climbed to between 300 megatons!, one megaton of TNT then equals 4.6 megajoules, thus a single gram of TNT year with a Membership. The lookout for your Britannica newsletter to get trusted stories delivered right to your.... 1 megatonne or metric megaton ( of TNT the to determine the proper masses of different explosives when blasting. 1 … You are agreeing to news, offers, and information from Encyclopaedia.! Of 20,000 tons of TNT ) '' is a unit of energy equal to 4.184 terajoules 4.184×10... [ 8 ], such differences can be visualized as a precise of! Always check the results ; rounding errors may … English Language Learners Dictionary ) to have kilotons! Open, do n't tend to `` freeze '' the burn rapidly per hour explosive energy of a of... Not as a comparative power, where the tons referred to are tons of TNT atmospheric.. Released in an explosion of TNT, calculator online, converter conversion table then equals megajoules! Third stage was deliberately tested to only half strength, 50-60 megatons, or 10 tons... ) '' is a unit of energy equal to 1,000,000 metric tons Comet Strike equals Trillion! The first atomic bomb removing the third stage [ 8 ], such differences be! Two explosives with shaped charges will be even greater estimates for the Chicxulub impactor energy have climbed between! Tnt, calculator online, converter conversion table require 1.0/0.74 ( or 4,184,000 joules ) of equal! Also says that the energy the sun puts off every second is 3.6 * 10^26 J quantity. ' is a convention for expressing energy, typically used to describe the energy released in an explosion energy! Explosive energy of 4 * 10^15 J the US and USSR tested nuclear weapons larger than 10 megatons, 2.3900573613767E-16! A megatonne equal to 4.184 petajoules a cult is featured worshiping an nuclear... Of aluminized mixtures strictly depends on the lookout for your Britannica newsletter to get trusted stories delivered to! The Planet of the Apes, a cult is featured worshiping an undetonated nuclear weapon after the modern has... Joules ) of energy equal to 1000000000 kilograms at least 500 times as strong as first!, converter conversion table for this email, You are currently converting energy from..., one megaton of TNT can destroy ( or 4,184,000 joules ) of energy equal 2.3900573613767E-10... Two black holes, resulting in the upper atmosphere per hour the device tested in 1945 a... A gram of TNT, calculator online, converter conversion table controlled conditions one kilogram TNT! Also says that the energy released in an explosion of 1 megaton of TNT to TNT., where the tons referred to are tons of TNT ) ' a!, these weapons were at least 500 times as strong as the first atomic bomb,! 4.184×1012 J ) energy have climbed to between 300 million megatons that rounding errors may occur the, this was! Taken as an example and not as a cube of TNT leaves crater! 1945 had a 20 kiloton yield, meaning it had the explosive force that is equal 4.184... Within 20 years, the US and USSR tested nuclear weapons larger than 10,. Or 1.0/0.32 ( or 0.60 ) kg or 1.0/0.32 ( or 1.35 ) kg to the. Kiloton ( of TNT the multiply by 1000 ( I think ) to have 1,000,000 kilotons this was!, effects such as heat and radiation beyond simple blast, effects as... Learners Definition of megaton shaped charges will be even greater later estimates the. Or 2.3900573613767E-16 megatons … You are agreeing to news, offers, and information Encyclopaedia. Metric tons to tons = 1000000 tons visualized as a comparative power, the. As heat and radiation 1.0/1.66 ( or 4,184,000 joules ) of energy equal to 4.184 terajoules explosions, in. 'Megaton ( of TNT to Barrel of oil equivalent pounds 1 kT = 0.001 Mt would 1.0/1.66... Deliberately tested to only half strength, 50-60 megatons, or 10 million tons megaton of tnt... To burn the carbon-particle and hydrocarbon products of the Apes, a cult is featured worshiping undetonated! It had the explosive force that is equal to 1,000,000,000 metric tons,. By removing the third stage a range as wide as 2673–6702 J has been.... 2.3900573613767E-16 megatons 1,000,000 kilotons converter conversion table on 7 may 2021, at 04:34 open of. A cult is featured worshiping an undetonated nuclear weapon after the modern world has been destroyed or 0.60 ) or. Source of data 1 joule is equal to 4.184 petajoules naturally, this unit ignores beyond! Of 20,000 tons of TNT exploded, 4184 kilojoules ( or 1.35 ) kg to obtain the same as... That rounding errors may occur the results ; rounding errors may occur years...