TheInfoList

The long and short scales are two of several naming systems for integer
powers of ten 480px, Visualisation of powers of 10 from one to 1 billion. A power of 10 is any of the integer An integer (from the Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European langu ...
which use some of the same terms for different magnitudes. For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two scales are identical. For larger numbers, starting with 109, the two systems differ. For identical names, the long scale proceeds by powers of one million, whereas the short scale proceeds by powers of one thousand. For example, "one billion" means one thousand millions in the short scale, while it means one million millions in the long scale. The long scale system uses additional terms for the intervening values, typically replacing the word ending ''-ion'' with ''-iard''.

# Scales

In both short and long scale naming, names are given each multiplication step for increments of the base-10 exponent of three, i.e. for each integer ''n'' in the sequence of multipliers 103n. For certain multipliers, including those for all numbers smaller than 109, both systems use the same names. The differences arise from the assignment of identical names to specific values of ''n'', for numbers starting with 109, for which ''n''=3. In the short scale system, the identical names are for ''n''=3, 4, 5, ..., while the long scale places them at ''n''=4, 6, 8, etc.

## Short scale

In the short scale, ''
billion A billion is a number with two distinct definitions: *1,000,000,000 1,000,000,000 (one billion, short scale; one thousand million or milliard, yard, long scale) is the natural number In mathematics, the natural numbers are those used for ...

'' means a thousand millions (''1,000,000,000'' which is 109), ''
trillion A trillion is a number with two distinct definitions: * 1,000,000,000,000, i.e. one million million, or (ten to the twelfth power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted ...
'' means one thousand billions (1012), and so on. Thus, an ''n''-illion equals 103''n''+3.

## Long scale

In the long scale, ''billion'' means one million millions (1012) and ''trillion'' means one million billions (1018), and so on. Therefore, an ''n''-illion equals 106''n''. In some languages, the long scale uses additional names for the interleaving multipliers, replacing the ending ''-ion'' with ''-iard''; for example, the next multiplier after ''million'' is ''milliard'', after ''billion'' it is ''billiard''. Hence, an ''n''-iard equals 106''n''+3.

# Use

Countries with usage of the long scale include most countries in
continental Europe Continental Europe or mainland Europe is the contiguous continent A continent is any of several large landmasses. Generally identified by convention (norm), convention rather than any strict criteria, up to seven geographical region ...

, and most that are
French-speaking French ( or ) is a Romance language The Romance languages (less commonly Latin languages, or Neo-Latin languages) are the modern languages that evolved from Vulgar Latin between the third and eighth centuries. They are a subgroup of t ...
,
German-speaking The German language (, ) is a West Germanic language mainly spoken in Central Europe Central Europe is the central region of Europe. Central Europe includes contiguous territories that are sometimes also considered parts of Western Europe ...
,
Spanish-speaking Hispanophone and Hispanic refers to anything relating to the speech of Spain (the ''Hispanosphere''). In a cultural, rather than merely linguistic sense, the notion of "Hispanophone" goes further than the above definition. The Hispanic culture is t ...
and
Portuguese-speaking countries The Community of Portuguese Language Countries ( Portuguese: ''Comunidade dos Países de Língua Portuguesa''; abbreviated as the CPLP), also known as the Lusophone Commonwealth (''Comunidade Lusófona''), is an international organization and pol ...
(except
Brazil Brazil ( pt, Brasil; ), officially the Federative Republic of Brazil (Portuguese: ), is the largest country in both and . At 8.5 million square kilometers (3.2 million square miles) and with over 211 million people, Brazil is the ...

). The short scale is used in most English-speaking and
Arabic-speaking countries Arabic Arabic (, ' or , ' or ) is a Semitic language that first emerged in the 1st to 4th centuries CE.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet ...
, in
Brazil Brazil ( pt, Brasil; ), officially the Federative Republic of Brazil (Portuguese: ), is the largest country in both and . At 8.5 million square kilometers (3.2 million square miles) and with over 211 million people, Brazil is the ...

, and in several other countries. Number names are rendered in the language of the country, but are similar due to shared
etymology Etymology ()The New Oxford Dictionary of English ''The'' () is a grammatical article Article often refers to: * Article (grammar) An article is any member of a class of dedicated words that are used with noun phrases to mark the identif ...
. Some languages, particularly in
East Asia East Asia is the eastern region of Asia Asia () is Earth's largest and most populous continent, located primarily in the Eastern Hemisphere, Eastern and Northern Hemisphere, Northern Hemisphere of the Earth, Hemispheres. It shares the ...

and
South Asia South Asia is the southern region of Asia Asia () is Earth's largest and most populous continent, located primarily in the Eastern Hemisphere, Eastern and Northern Hemisphere, Northern Hemisphere of the Earth, Hemispheres. It shares the ...

, have large number naming systems that are different from both the long and short scales, for example the
Indian numbering system The Indian numbering system is used in the Indian subcontinent (Bangladesh Bangladesh (; bn, বাংলাদেশ, ), officially the People's Republic of Bangladesh, is a country in South Asia. It is the List of countries and dependen ...
. For most of the 19th and 20th centuries, the
United Kingdom The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain,Usage is mixed. The Guardian' and Telegraph' use Britain as a synonym for the United Kingdom. Some prefer to use Britain as shorth ...

largely used the long scale, whereas the
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country in . It consists of 50 , a , five major , 326 , and some . At , it is the world's . The United States shares significan ...

used the short scale, so that the two systems were often referred to as ''British'' and ''American'' in the
English language English is a of the , originally spoken by the inhabitants of . It is named after the , one of the ancient that migrated from , a peninsula on the (not to be confused with ), to the area of later named after them: . Living languages mos ...

. After several decades of increasing informal British usage of the short scale, in 1974 the government of the UK adopted it, and it is used for all official purposes. With very few exceptions, the British usage and American usage are now identical. The first recorded use of the terms ''short scale'' (french: échelle courte) and ''long scale'' (french: échelle longue) was by the French mathematician Geneviève Guitel in 1975. To avoid confusion resulting from the coexistence of short and long term in any language, the
International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' (Kevin Michael album), 2011 * International (New Order album), '' ...
(SI) recommends using the
metric prefix A metric prefix is a unit prefixA unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various order of magnitude, sizes are commonly formed by the use of such ...
to indicate orders of magnitude, but it is only relevant to scientific applications, and not (for example) to finance. Unlike words like billion and trillion, metric prefixes keep the same meaning regardless of the country and the language.

# Comparison

The relationship between the numeric values and the corresponding names in the two scales can be described as: The relationship between the names and the corresponding numeric values in the two scales can be described as: The root ''mil'' in ''million'' does not refer to the numeral, ''1''. The word, ''million'', derives from the Old French, ''milion'', from the earlier Old Italian, ''milione'', an intensification of the Latin word, ''mille'', a thousand. That is, a ''million'' is a ''big thousand'', much as a ''
great gross 1728 is the natural number In mathematics, the natural numbers are those used for counting (as in "there are ''six'' coins on the table") and total order, ordering (as in "this is the ''third'' largest city in the country"). In common mathemat ...
'' is a dozen gross or 12 × 144 =
1728 Events January–March * January 5 Events Pre-1600 * 1477 – Battle of Nancy: Charles the Bold is defeated and killed in a conflict with René II, Duke of Lorraine; the Duchy of Burgundy, Burgundy subsequently becomes par ...
. The word ''milliard'', or its translation, is found in many European languages and is used in those languages for 109. However, it is not found in American English, which uses ''billion'', and not used in British English, which preferred to use ''thousand million'' before the current usage of ''billion''. The financial term ''yard'', which derives from ''milliard'', is used on financial markets, as, unlike the term ''billion'', it is internationally unambiguous and phonetically distinct from ''million''. Likewise, many long scale countries use the word ''billiard'' (or similar) for one thousand long scale billions (i.e., 1015), and the word ''trilliard'' (or similar) for one thousand long scale trillions (i.e., 1021), etc.

# History

The existence of the different scales means that care must be taken when comparing large numbers between languages or countries, or when interpreting old documents in countries where the dominant scale has changed over time. For example, British English, French, and Italian historical documents can refer to either the short or long scale, depending on the date of the document, since each of the three countries has used both systems at various times in its history. Today, the United Kingdom officially uses the short scale, but
France France (), officially the French Republic (french: link=no, République française), is a spanning and in the and the , and s. Its extends from the to the and from the to the and the ; overseas territories include in , in the N ...

and
Italy Italy ( it, Italia ), officially the Italian Republic ( it, Repubblica Italiana, links=no ), is a country consisting of delimited by the and surrounding it, whose territory largely coincides with the . Italy is located in the centre of th ...

use the long scale. The pre-1974 former British English word ''billion'', post-1961 current French word ''billion'', post-1994 current Italian word ''bilione'', Spanish ''billón'', German ''Billion'', Dutch ''biljoen'', Danish ''billion'', Swedish ''biljon'', Finnish ''biljoona'', Slovenian ''bilijon'', Polish ''bilion'', and European Portuguese word ''bilião'' (with a different spelling to the Brazilian Portuguese variant, but in Brazil referring to short scale) all refer to 1012, being long-scale terms. Therefore, each of these words translates to the American English or post-1974 British English word: ''trillion'' (1012 in the short scale), and not ''billion'' (109 in the short scale). On the other hand, the pre-1961 former French word ''billion'', pre-1994 former Italian word ''bilione'', Brazilian Portuguese word ''bilhão'', and Welsh word ''biliwn'' all refer to 109, being short scale terms. Each of these words translates to the American English or post-1974 British English word ''billion'' (109 in the short scale). The term ''billion'' originally meant 1012 when introduced. * In long scale countries, ''milliard'' was defined to its current value of 109, leaving ''billion'' at its original 1012 value and so on for the larger numbers. Some of these countries, but not all, introduced new words ''billiard'', ''trilliard'', etc. as intermediate terms. * In some short scale countries, ''milliard'' was defined to 109 and ''billion'' dropped altogether, with ''trillion'' redefined down to 1012 and so on for the larger numbers. * In many short scale countries, ''milliard'' was dropped altogether and ''billion'' was redefined down to 109, adjusting downwards the value of ''trillion'' and all the larger numbers. ;Timeline }) and ''short scale'' (french: échelle courte) to refer to the two numbering systems. , - , valign="top", 1994 , The
Italian Government The Government of Italy is in the form of a democratic republic, and was established by a constitution in 1948. It consists of legislative, Executive (government), executive, and judicial subdivisions, as well as a Head of State, or President. A ...
confirmed their official usage of the long scale. As large numbers in natural sciences are usually represented by metric prefixes, scientific notation or otherwise, the most commonplace occurrence of large numbers represented by long or short scale terms is in finance. The following table includes some historic examples related to hyper-inflation and other financial incidents. ;Timeline

# Current usage

## Short scale users

### English-speaking

Most English-language countries and regions use the short scale with 109 being ''billion''. For example: * * * * * * * (English-speaking) * * (English-speaking) * * (English-speaking) * (English-speaking) ''see'' Using both ''below'' * * * * * (formerly ''Swaziland'') * * * * * (English-speaking) * * * * * (English-speaking) * (English-speaking) * (English-speaking, ga, billiún, ''trilliún'') * * * * (English-speaking) * * * * (English-speaking) * (English-speaking; ms, bilion billion, trillion) * (English-speaking; mt, biljun, * * (English speaking) ''see'' Using both ''below'' * * * * * (English-speaking) * * * * * (English-speaking) * (English-speaking) * * * * * * * * (English speaking) ''see'' Using both ''below'' * * (English-speaking) * * * (English-speaking) * (English-speaking) * * * * * * (English-speaking) * (''see also'' Wales ''below'') * * * (English speaking) ''see'' Using both ''below'' * (English-speaking) * (English-speaking)

### Arabic-speaking

Most
Arabic-language Arabic (, ' or , ' or ) is a Semitic languages, Semitic language that first emerged in the 1st to 4th centuries CE.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Stre ...

countries and regions use the short scale with 109 being , except for a few countries like Saudi Arabia and the UAE which use the word بليون for 109. For example: * * * * * * * * * * * * * * * * * * * * * * * * *

### Other short scale

Other countries also use a word similar to ''trillion'' to mean 1012, etc. Whilst a few of these countries like English use a word similar to ''billion'' to mean 109, most like Arabic have kept a traditional long scale word similar to ''milliard'' for 109. Some examples of short scale use, and the words used for 109 and 1012, are * (
Dari Dari (, , ), or Dari Persian (, ), is a political term used for the various dialects of the Persian language Persian (), also known by its endonym An endonym (from Greek: , 'inner' + , 'name'; also known as autonym) is a common, interna ...
: or , ,
Pashto Pashto (,; / , ), sometimes spelled Pukhto or Pakhto, is an Eastern Iranian language The Eastern Iranian languages are a subgroup of the Iranian languages The Iranian or Iranic languages are a branch of the Indo-Iranian languages in ...
: , بیلیون , ) * (, ) * ( , ) * (, () * ( , ) * (
Brazilian Portuguese Brazilian Portuguese (', or ' ) or also ' is the set of dialect The term dialect (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spok ...
: , ) * ( ms, bilion, ) * ( , ) * (
Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 million as of ...
: , , tr, milyar, ) * ( or , ) * ( , ) * (, ) * (
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: , ) * ( Kazakh: , ) * (
KyrgyzKyrgyz, Kirghiz or Kyrgyzstani may refer to: *Things related to Kyrgyzstan *Kyrgyz people *Kyrgyz language *Kyrgyz culture *Kyrgyz cuisine *Yenisei Kirghiz *The Fuyu Kyrgyz language, Fuyü Gïrgïs language in Northeastern China {{Disambig Languag ...
: , ) * (, ) * (, ) * (
Romanian Romanian may refer to: *anything of, from, or related to the country and nation of Romania Romania ( ; ro, România ) is a country at the crossroads of Central Europe, Central, Eastern Europe, Eastern and Southeast Europe, Southeastern Euro ...
: , ) * (formerly ''Burma'') ( Burmese: , ; , ) * (Afrikaans speaking) ''see'' Using both ''below'' * (Spanish speaking) ''see'' Using both ''below'' * ( , ) * ( Tajik: , ) * (, ) * ( Turkmen: , ; Russian: , ) * (Afrikaans speaking) ''see'' Using both ''below'' * ( , ) * (: , ; Russian: , ) * (, ) (In some contexts a paraphrase is needed to resolve ambiguity, as the lenitive of both and is the same: .)

## Long scale users

The traditional long scale is used by most
Continental Europe Continental Europe or mainland Europe is the contiguous continent A continent is any of several large landmasses. Generally identified by convention (norm), convention rather than any strict criteria, up to seven geographical region ...

an countries and by most other countries whose languages derive from
Continental Europe Continental Europe or mainland Europe is the contiguous continent A continent is any of several large landmasses. Generally identified by convention (norm), convention rather than any strict criteria, up to seven geographical region ...

(with the notable exceptions of Albania, Greece, Romania, and Brazil). These countries use a word similar to ''billion'' to mean 1012. Some use a word similar to ''milliard'' to mean 109, while others use a word or phrase equivalent to ''thousand millions''.

### Dutch-speaking

Most
Dutch-language Dutch is a West Germanic languages, West Germanic language spoken by about 24 million people as a first language and 5 million people as a second language, constituting the majority of people in the Netherlands (where it is the only official la ...
countries and regions use the long scale with 109 = , for example: * * * * * *

### French-speaking

Most
French-language French ( or ) is a Romance language The Romance languages (less commonly Latin languages, or Neo-Latin languages) are the modern languages that evolved from Vulgar Latin between the third and eighth centuries. They are a subgroup of t ...

countries and regions use the long scale with 109 = , for example: * * * * (
Canadian French Canadian French (french: français canadien) is the French language French ( or ) is a Romance language The Romance languages, less commonly Latin or Neo-Latin languages, are the modern languages that evolved from Vulgar Latin ...
) ''see'' Using both ''below'' * * * * * * * * * * (Côte d'Ivoire) * * * * * (province of Canada,
Canadian French Canadian French (french: français canadien) is the French language French ( or ) is a Romance language The Romance languages, less commonly Latin or Neo-Latin languages, are the modern languages that evolved from Vulgar Latin ...
) ''see'' Using both ''below'' * * (French portion of St. Martin Island) * * *

### German-speaking

German-language countries and regions use the long scale with 109 = , for example: * * * *

### Portuguese-speaking

With the notable exception of Brazil, a short scale country, most countries and regions use the long scale with 109 = ''or'' , for example: * * * * * * * *

### Spanish-speaking

Most
Spanish-language Spanish () or Castilian (, ) is a Romance language The Romance languages (less commonly Latin languages, or Neo-Latin languages) are the modern languages that evolved from Vulgar Latin between the third and eighth centuries. They are a sub ...

countries and regions use the long scale, for example: * * * * * * * * * * * () * () * ( or ) * ( or ) * ( or ) * * () * ''see'' Using both ''below'' * ( or typ. ) * *

### Other long scale

Some examples of long scale use, and the words used for 109 and 1012, are * ( ca, miliard or typ. , ) * ( bs, milijarda, ; hr, milijarda, , sr, милијарда , ) * (, ) * (, ) * (, ) *
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(, ) * (, ) * ( fi, miljardi, ; Swedish: , ) * (, ) * (, or ) * (, ) * (
Persian Persian may refer to: * People and things from Iran, historically called ''Persia'' in the English language ** Persians, Persian people, the majority ethnic group in Iran, not to be conflated with the Iranian peoples ** Persian language, an Iranian ...
: میلیارد , بیلیون , تریلیون ) * (, ) * (French: , ; German: , ; lb, milliard, ) * (French: , ; mg, miliara, ) * (English speaking) ''see'' Using both ''below'' * ( Montenegrin: , ) * (Afrikaans speaking) ''see'' Using both ''below'' * ( , ) * (
Bokmål Bokmål (, ; literally "book tongue") is an official written standard for the Norwegian language Norwegian (Norwegian: ''norsk'') is a North Germanic languages, North Germanic language spoken mainly in Norway, where it is an official language. A ...
: , ;
Nynorsk Nynorsk (translates to “Modern Norwegian”, literally “New Norwegian”) is one of the two written standards of the Norwegian language, the other being Bokmål. From 12 May 1885, it became the state-sanctioned version of Ivar Aasen's standa ...
: , ) * (, ) * (, ). There are ambiguities for numbers above 1012. * (Italian: , ) * ( , ) * (English speaking) ''see'' Using both ''below'' * (, ) * (, ) * (Afrikaans speaking) ''see'' Using both ''below'' * (, ) * (French: , ;
German German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany or people of German ancestry * For citizens of Germany, see also German nationality law * German language The German la ...
: , ; Italian: , ; Romansh: , ) * (Italian: , ) * (English speaking) ''see'' Using both ''below''

## Using both

Some countries use either the short or long scales, depending on the internal language being used or the context.

## Using neither

The following countries use naming systems for large numbers that are not etymologically related to the short and long scales:

## By continent

The long and short scales are both present on most continents, with usage dependent on the language used. Examples include:

# Alternative approaches

Unambiguous ways of identifying large numbers include: * In written communications, the simplest solution for moderately large numbers is to write the full amount, for example 1,000,000,000,000 rather than, say, 1 trillion (short scale) or 1 billion (long scale). * Combinations of the unambiguous word ''million'', for example: 109 = "one thousand million"; 1012 = "one million million". This becomes rather unwieldy for numbers above 1012. * Combination of numbers of more than 3 digits with the unambiguous word ''million'', for example 13,600 million *
Scientific notation Scientific notation is a way of expressing numbers A number is a mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is anything that has been (or coul ...
(also known as standard form or exponential notation, for example 1, 1, 1, 1, etc.), or its
engineering notation Engineering notation or engineering form is a version of scientific notation in which the exponent of ten must be divisible by three (i.e., they are powers of a thousand, but written as, for example, 106 instead of 10002). As an alternative to writi ...
variant (for example 1, 10, 100, 1, etc.), or the computing variant
E notation Scientific notation is a way of expressing real numbers, numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard in ...
(for example `1e9`, `1e10`, `1e11`, `1e12`, etc.). This is the most common practice among scientists and mathematicians, and is both unambiguous and convenient. *
SI prefix The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wi ...
es in combination with
SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system The metric system is a that succeeded the decimal ...
s, for example,
giga Giga ( or ) is a unit prefixA unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various order of magnitude, sizes are commonly formed by the use of such prefi ...
for 109 and
tera Tera or TERA may refer to: People * Tera Patrick Tera Patrick (born Linda Ann Hopkins July 25, 1976) is an American former pornographic film actor, pornographic actress and model who was the ''Penthouse (magazine), Penthouse'' Pet of the M ...
for 1012 can give
gigawatt The watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equa ...
(=109 W) and
terawatt The watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equa ...
(=1012 W), respectively. The
International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' (Kevin Michael album), 2011 * International (New Order album), '' ...
(SI) is independent of whichever scale is being used. Use with non-SI units (e.g. "giga-dollars", "giga-miles") is uncommon although "megabucks" is in informal use representing a large sum of money rather than exactly a million dollars. k€ and M€ is more frequently encountered, although the official scheme places the
Euro sign The euro sign () is the currency sign A currency symbol or currency sign is a graphic symbol used as a shorthand for a currency's name, especially in reference to amounts of money. Usage When writing currency amounts, the location of the symb ...

in front of the value. The SI-approach has the advantage to survive translations without ambiguity and is well understood in an IT context, especially in countries that have established SI-standards.

*
Googol A googol is the large number Numbers that are significantly larger than those typically used in everyday life, for instance in simple counting or in monetary transactions, appear frequently in fields such as mathematics Mathematics (fro ...

(number) *
Googolplex A googolplex is the number 10, or equivalently, 10. Written out in ordinary decimal notation The decimal numeral system A numeral system (or system of numeration) is a writing system A writing system is a method of visually represent ...
(number) *
Names of large numbers This article lists and discusses the usage and derivation of names of large numbers Numbers that are significantly larger than those typically used in everyday life, for instance in simple counting or in monetary transactions, appear frequently ...
* Names of small numbers *
Orders of magnitude (numbers) This list contains selected positive number A number is a mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is anything that has been (or could be) forma ...
*
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which displays some similar issues