「ローマ数字」の版間の差分

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2018年1月22日 (月) 13:21 の版に戻す
18行目:
| style="width:3em" | [[D|{{Rn|D}}]]
| style="width:3em" | [[M|{{Rn|M}}]]
| style="width:3em" | [[N|{{Rn|N}}]]
| style="width:3em" | [[H|{{Rn|H}}]]
| style="width:3em" | [[P|{{Rn|P}}]]
| style="width:3em" | [[T|{{Rn|T}}]]
| style="width:3em" | [[J|{{Rn|J}}]]
| style="width:3em" | [[S|{{Rn|S}}]]
| style="width:3em" | [[G|{{Rn|G}}]]
| style="width:3em" | [[W|{{Rn|W}}]]
| style="width:3em" | [[F|{{Rn|F}}]]
| style="width:3em" | [[Y|{{Rn|Y}}]]
| style="width:3em" | [[B|{{Rn|B}}]]
| style="width:3em" | [[Q|{{Rn|Q}}]]
|-
! アラビア数字
| [[1]] || [[5]] || [[10]] || [[50]] || [[100]] || [[500]] || [[1000]] || [[5000]] || [[10,000]] || [[50,000]] || [[100,000]] || [[500,000]] || [[1,000,000]] || [[5,000,000]] || [[10,000,000]] || [[50,000,000]] || [[100,000,000]] || [[500,000,000]] || [[1,000,000,000]]
|}
 
これ以外の数は基本的にこれらの加算で表現され、加算すべき数を、できるだけ使う文字数が少なくなるように選び、左から大きい順に並べて書く。
 
47 ⟶ 34行目:
| style="width:3em" | {{Rn|CD}}
| style="width:3em" | {{Rn|CM}}
| style="width:3em" | {{Rn|MN}}
| style="width:3em" | {{Rn|MH}}
| style="width:3em" | {{Rn|HP}}
| style="width:3em" | {{Rn|HT}}
| style="width:3em" | {{Rn|TJ}}
| style="width:3em" | {{Rn|TS}}
| style="width:3em" | {{Rn|SG}}
| style="width:3em" | {{Rn|SW}}
| style="width:3em" | {{Rn|WF}}
| style="width:3em" | {{Rn|WY}}
| style="width:3em" | {{Rn|YB}}
| style="width:3em" | {{Rn|YQ}}
|-
! アラビア数字
| [[4]] || [[9]] || [[40]] || [[90]] || [[400]] || [[900]] || [[4000]] || [[9000]] || [[40,000]] || [[90,000]] || [[400,000]] || [[900,000]] || [[4,000,000]] || [[9,000,000]] || [[40,000,000]] || [[90,000,000]] || [[400,000,000]] || [[900,000,000]]
|}
これらの数は減算則を使わず表現することも可能(例:4 を「{{Rn|IIII}}」、9を「{{Rn|VIIII}}」)だが、通常は減算則を用いて表記する。なお、減算則が認められるのは'''同じ文字を4つ以上連続で並べるのを避けるためだけ'''であり、それ以外で使うことは認められていない。また、減算則を使う場合でも認められているのは{{Rn|I}} を大きくても <!--{{Rn|V}}または-->{{Rn|X}} までの左に、{{Rn|X}} を <!--{{Rn|L}}または-->{{Rn|C}} までの左に、{{Rn|C}} を <!--{{Rn|D}}または-->{{Rn|M}} までの左に、{{Rn|M}} を <!--{{Rn|N}}または-->{{Rn|H}} までの左に、{{Rn|H}} を を <!--{{Rn|P}}または-->{{Rn|T}} までの左に、{{Rn|T}} を を <!--{{Rn|J}}または-->{{Rn|S}} までの左に、{{Rn|S}} <!--{{Rn|G}}または-->{{Rn|W}} までの左に、{{Rn|W}} を <!--{{Rn|F}}または-->{{Rn|Y}} までの左に、{{Rn|Y}} を <!--{{Rn|B}}または-->{{Rn|Q}} を までの左に 1 つだけおのおの置く計6種類だけであり、それ以外の使い方は認められていない。また、{{math|5 × 10{{sup|''n''}}}} を表す{{Rn|V}}、{{Rn|L}}、{{Rn|D}}は1つの数字の中で多くても1回までしか使うことができないため、例えば9を「{{Rn|VIV}}」<!--(5+(−1+5))-->、90を「{{Rn|LXL}}」<!--(50+(-10+50))-->と表記することは認められていない。したがって、例えば2者の商が10または1/10であるからと言って45を「{{Rn|VL}}」<!--(−5 + 50)-->、451を「{{Rn|LDI}}」<!--((−50 + 500) + 1)--><!--、295を「{{Rn|CCVC}}」、2950を「{{Rn|MMLM}}」-->と表記することさえ認められていない。と言うのも、例えば「{{Rn|LD}}」を450と同一視。それを使って491をローマ数字にコンヴァートすると「{{Rn|LDXLI}}」となり、{{Rn|L}}を2回使っている事になるため。
 
以上を踏まえると、1 から 9 およびその 10 倍と100 倍と1000 倍と10,000 倍と100,000 倍 倍と1,000,000 倍と10,000,000 倍と100,000,000 倍、1,000,000,00010002,000,000,00020003,000,000,0003000は以下のような表記となる。なお、'''[[0]] を表す表記は存在しない'''。
 
{| class="wikitable" style="text-align:center"
71 ⟶ 46行目:
| {{Rn|X}}|| {{Rn|XX}}|| {{Rn|XXX}}|| {{Rn|XL}}|| {{Rn|L}}|| {{Rn|LX}}|| {{Rn|LXX}}|| {{Rn|LXXX}}|| {{Rn|XC}}
| {{Rn|C}}|| {{Rn|CC}}|| {{Rn|CCC}}|| {{Rn|CD}}|| {{Rn|D}}|| {{Rn|DC}}|| {{Rn|DCC}}|| {{Rn|DCCC}}|| {{Rn|CM}}
| {{Rn|M}}|| {{Rn|MM}}|| {{Rn|MMM}}|| {{Rn|MN}}|| {{Rn|N}}|| {{Rn|NM}}|| {{Rn|NMM}}|| {{Rn|NMMM}}|| {{Rn|MH}}
| {{Rn|H}}|| {{Rn|HH}}|| {{Rn|HHH}}|| {{Rn|HP}}|| {{Rn|P}}|| {{Rn|PH}}|| {{Rn|PHH}}|| {{Rn|PHHH}}|| {{Rn|HT}}
| {{Rn|T}}|| {{Rn|TT}}|| {{Rn|TTT}}|| {{Rn|TJ}}|| {{Rn|J}}|| {{Rn|JT}}|| {{Rn|JTT}}|| {{Rn|JTTT}}|| {{Rn|TS}}
| {{Rn|S}}|| {{Rn|SS}}|| {{Rn|SSS}}|| {{Rn|SG}}|| {{Rn|G}}|| {{Rn|GS}}|| {{Rn|GSS}}|| {{Rn|GSSS}}|| {{Rn|SW}}
| {{Rn|W}}|| {{Rn|WW}}|| {{Rn|WWW}}|| {{Rn|WF}}|| {{Rn|F}}|| {{Rn|FW}}|| {{Rn|FWW}}|| {{Rn|FWWW}}|| {{Rn|WY}}
| {{Rn|Y}}|| {{Rn|YY}}|| {{Rn|YYY}}|| {{Rn|YB}}|| {{Rn|B}}|| {{Rn|BY}}|| {{Rn|BYY}}|| {{Rn|BYYY}}|| {{Rn|YQ}}
| {{Rn|Q}}|| {{Rn|QQ}}|| {{Rn|QQQ}}
|-
| 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9
| 10 || 20 || 30 || 40 || 50 || 60 || 70 || 80 || 90
| 100 || 200 || 300 || 400 || 500 || 600 || 700 || 800 || 900
| 1000 || 2000 || 3000 || 4000 || 5000 || 6000 || 7000 || 8000 || 9000
| 10,000 || 20,000 || 30,000 || 40,000 || 50,000 || 60,000 || 70,000 || 80,000 || 90,000
| 100,000 || 200,000 || 300,000 || 400,000 || 500,000 || 600,000 || 700,000 || 800,000 || 900,000
| 1,000,000 || 2,000,000 || 3,000,000 || 4,000,000 || 5,000,000 || 6,000,000 || 7,000,000 || 8,000,000 || 9,000,000
| 10,000,000 || 20,000,000 || 30,000,000 || 40,000,000 || 50,000,000 || 60,000,000 || 70,000,000 || 80,000,000 || 90,000,000
| 100,000,000 || 200,000,000 || 300,000,000 || 400,000,000 || 500,000,000 || 600,000,000 || 700,000,000 || 800,000,000 || 900,000,000
| 1,000,000,000 || 2,000,000,000 || 3,000,000,000
|}
これを組み合わせることで、1 から 3,999,999,9993999 の値が表現できる。
 
== ローマ数字の並べ方の例 ==
161 ⟶ 124行目:
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|MMMCMXCIX}}
|-
| 4205 || = || (-1000 + 5000) || + || 100 × 2 || + || 5
|-
| &nbsp; || = || {{Rn|MN}} || + || {{Rn|CC}} || + || {{Rn|V}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|MNCCV}}
|-
| 12,167 || = || 10,000 || + || (1000 × 2) || + || 100 || + || 50 || + || 10 || + || (1 × 2)
|-
| &nbsp; || = || {{Rn|H}} || + || {{Rn|MM}} || + || {{Rn|C}} || + || {{Rn|L}} || + || {{Rn|X}} || + || {{Rn|V}} || + || {{Rn|II}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|HMMCLXVII}}
|-
| 20,650 || = || (10,000 × 2) || + || 500 || + || 100 || + || 50
|-
| &nbsp; || = || {{Rn|HH}} || + || {{Rn|D}} || + || {{Rn|C}} || + || {{Rn|L}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|HHDCL}}
|-
| 29,765 || = || (10,000 × 3) || + || (-1000 + 1000) || + || 100 × 2 || + || 500 || + || 50 || + || 10 || + || 5
|-
| &nbsp; || = || {{Rn|HH}} || + || {{Rn|MH}} || + || {{Rn|D}} || + || {{Rn|CC}} || + || {{Rn|L}} || + || {{Rn|X}} || + || {{Rn|V}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|HHMHDCCLXV}}
|-
| 35,899 || = || (10,000 × 3) || + || 5000 || + || 500 || + || 100 × 3 || + || (-10 + 100) || + || (-1 + 10)
|-
| &nbsp; || = || {{Rn|HHH}} || + || {{Rn|N}} || + || {{Rn|D}} || + || {{Rn|CCC}} || + || {{Rn|XC}} || + || {{Rn|IX}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|HHHNDCCCXCIX}}
|-
| 46,853 || = || (-10,000 + 50,000) || + || 5000 || + || 1000 || + || 500 || + || (100 × 3) || + || 50 || + || (1 × 3)
|-
| &nbsp; || = || {{Rn|HP}} || + || {{Rn|N}} || + || {{Rn|M}} || + || {{Rn|D}} || + || {{Rn|CCC}} || + || {{Rn|L}} || + || {{Rn|III}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|HPNMDCCCLIII}}
|-
| 183,230 || = || 100,000 || + || 50,000 || + || (10,000 × 3) || + || (1000 × 3) || + || (100 × 2) || + || (10 × 3)
|-
| &nbsp; || = || {{Rn|T}} || + || {{Rn|P}} || + || {{Rn|HHH}} || + || {{Rn|MMM}} || + || {{Rn|CC}} || + || {{Rn|XXX}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|TPHHHMMMCCXXX}}
|-
| 823,543 || = || 500,000 || + || (100,000 × 3) || + || (10,000 × 2) || + || (1000 × 3) || + || 500 || + || (-10 + 50) || + || (1 × 3)
|-
| &nbsp; || = || {{Rn|J}} || + || {{Rn|TTT}} || + || {{Rn|HH}} || + || {{Rn|MMM}} || + || {{Rn|D}} || + || {{Rn|XL}} || + || {{Rn|III}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|JTTTHHMMMDXLIII}}
|-
| 2,687,529 || = || (1,000,000 × 2) || + || 500,000 || + || 100,000 || + || 50,000 || + || (10,000 × 3) || + || 5000 || + || (1000 × 2) || + || 500 || + || (10 × 2) || + || (-1 + 10)
|-
| &nbsp; || = || {{Rn|SS}} || + || {{Rn|J}} || + || {{Rn|T}} || + || {{Rn|P}} || + || {{Rn|HHH}} || + || {{Rn|N}} || + || {{Rn|MM}} || + || {{Rn|D}} || + || {{Rn|XX}} || + || {{Rn|IX}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|SSJTPHHHNMMDXXIX}}
|-
| 10,025,604 || = || 10,000,000 || + || (10,000 × 2) || + || 5000 || + || 500 || + || 100 || + || (-1 + 5)
|-
| &nbsp; || = || {{Rn|W}} || + || {{Rn|HH}} || + || {{Rn|N}} || + || {{Rn|D}} || + || {{Rn|C}} || + || {{Rn|IV}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|WHHNDCIV}}
|-
| 123,456,789 || = || 100,000,000 || + || (10,000,000 × 2) || + || (1,000,000 × 3) || + || (-100,000 + 500,000) || + || 50,000 || + || 5000 || + || 1000 || + || 500 || + || (100 × 2) || + || 50 || + || (10 × 3) || + || (-1 + 10)
|-
| &nbsp; || = || {{Rn|Y}} || + || {{Rn|WW}} || + || {{Rn|SSS}} || + || {{Rn|TJ}} || + || {{Rn|P}} || + || {{Rn|N}} || + || {{Rn|M}} || + || {{Rn|D}} || + || {{Rn|CC}} || + || {{Rn|L}} || + || {{Rn|XXX}} || + || {{Rn|IX}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|YWWSSSTJPNMDCCLXXXIX}}
|-
| 990,000,000 || = || (-100,000,000 + 1,000,000,000) || + || (-10,000,000 + 100,000,000)
|-
| &nbsp; || = || {{Rn|YQ}} || + || {{Rn|WY}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|YQWY}}
|-
| 3,999,999,999 || = || (1,000,000,000 × 3) || + || (-100,000,000 + 1,000,000,000) || + || (-10,000,000 + 100,000,000) || + || (-1,000,000 + 10,000,000) || + || (-100,000 + 1,000,000) || + || (-10,000 + 100,000) || + || (-1000 + 10,000) || + || (-100 + 1000) || + || (-10 + 100) || + || (-1 + 10)
|-
| &nbsp; || = || {{Rn|QQQ}} || + || {{Rn|YQ}}
|-
| &nbsp; || = || colspan="3" style="text-align:left" | {{Rn|QQQYQWYSWTSHTMHCMXCIX}}
|}
なお、手書きでは、[[大文字]]のローマ数字は上下の[[セリフ (文字)|セリフ]]をつなげて書くことが多い。「V」は上部のセリフをつなぎ、逆三角形(▽)のようになる。小文字ではセリフを書かない。
291 ⟶ 176行目:
| {{Rn|CCC}}<nowiki>|</nowiki>{{Rn|ƆƆƆ}}<nowiki>|</nowiki>{{Rn|ƆƆƆ}} = 150,000
|}
; つなぎ表記
: 通常のローマ数字に上線を付加することで、1,000倍を表現する。また二重上線では1,000,000倍となる。すなわち''n''重上線では{{math|1,000{{sup|n}}}}倍となる。
:* 4,000 = {{Rn|{{overline|IV}}}} = {{Rn|M{{overline|V}}}}<!--
:* 4,597 = {{Rn|M{{overline|V}}DXCXII}}-->
:* 5,300 = {{Rn|{{overline|V}}CCC}}
:* 6,723 = {{Rn|{{overline|VI}}DCCXXIII}} = {{Rn|{{overline|V}}MDCCXXIII}}
:* 9,999 = {{Rn|{{overline|IX}}CMXCIX}} = {{Rn|M{{overline|X}}CMXCIX}}
:* 51,200 = {{Rn|{{overline|LI}}CC}}
:* 99,999 = {{Rn|{{overline|XCIX}}CMXCIX}}
:* 500,000 = {{Rn|{{overline|D}}}}<span style="border-top:double">{{Rn|I}}
:* 921,600 = {{Rn|{{overline|C}}}}<span style="border-top:double">{{Rn|I}}</span>{{Rn|{{overline|XXI}}DC}}
:* 3,000,000 = <span style="border-top:double">{{Rn|III}}
:* 9,125,334 = <span style="border-top:double">{{Rn|IX}}</span>{{Rn|{{overline|CCXXV}}CCCXXXIV}}
:* 91,200,937 = <span style="border-top:double">{{Rn|XCI}}</span>{{Rn|{{overline|CC}}CMXXXVII}}
:* 235,002,011 = <span style="border-top:double">{{Rn|CCXXXV}}</span>{{Rn|{{overline|II}}XI}}
:
:さらに前後に縦線を付加し、さらに100倍(都合100,000倍)を表現する。
:* 800,000 = |{{Rn|{{overline|VIII}}}}|
:* 1,040,000 = |{{Rn|{{overline|X}}}}|{{Rn|{{overline|XL}}}} = <span style="border-top:double">{{Rn|I}}</span>{{Rn|{{overline|XL}}}}
 
== 用途 ==