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10,000,000,000,000

From Wikipedia, the free encyclopedia
Natural number
10000000000000
CardinalTen trillion (short scale)
Ten billion (long scale)
Ten thousand billion
Ten million million
Ordinal10000000000000th (ten trillionth, short scale)
Factorization
  • 213
  • 513
Divisors196 total
Greek numeralMι{\displaystyle {\stackrel {\iota }{\mathrm {M} }}}
Roman numeralN/A,n/a
Binary100100011000010011100111001010100000000000002
Ternary10221012222020120200202111013
Senary331335341450241446
Octal2214116345200008
Duodecimal115609792505412
Hexadecimal9184E72A00016
Arabic١٠٠٠٠٠٠٠٠٠٠٠٠٠
Bengali১০০০০০০০০০০০০০
Devanagari१०००००००००००००
Khmer១០០០០០០០០០០០០០
Tamilக௦௦௦௦௦௦௦௦௦௦௦௦௦
Thai๑๐๐๐๐๐๐๐๐๐๐๐๐๐ (สิบล้านล้าน)

10,000,000,000,000 (ten trillion on the short scale;ten billion on the long scale; ten thousandbillion; ten millionmillion) is thenatural number following9,999,999,999,999 and preceding 10,000,000,000,001. It is known as 10000 arab, 100 kharab, 10lakhcrore, or 1nil in theIndian numbering system.

Properties and usage

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10,000,000,000,000 has the following properties and usage:

In mathematics

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1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1000, 1024, 1250, 1280, 1600, 2000, 2048, 2500, 2560, 3125, 3200, 4000, 4096, 5000, 5120, 6250, 6400, 8000, 8192, 10000, 10240, 12500, 12800, 15625, 16000, 20000, 20480, 25000, 25600, 31250, 32000, 40000, 40960, 50000, 51200, 62500, 64000, 78125, 80000, 100000, 102400, 125000, 128000, 156250, 160000, 200000, 204800, 250000, 256000, 312500, 320000, 390625, 400000, 500000, 512000, 625000, 640000, 781250, 800000, 1000000, 1024000, 1250000, 1280000, 1562500, 1600000, 1953125, 2000000, 2500000, 2560000, 3125000, 3200000, 3906250, 4000000, 5000000, 5120000, 6250000, 6400000, 7812500, 8000000, 9765625, 10000000, 12500000, 12800000, 15625000, 16000000, 19531250, 20000000, 25000000, 25600000, 31250000, 32000000, 39062500, 40000000, 48828125, 50000000, 62500000, 64000000, 78125000, 80000000, 97656250, 100000000, 125000000, 128000000, 156250000, 160000000, 195312500, 200000000, 244140625, 250000000, 312500000, 320000000, 390625000, 400000000, 488281250, 500000000, 625000000, 640000000, 781250000, 800000000, 976562500, 1000000000, 1220703125, 1250000000, 1562500000, 1600000000, 1953125000, 2000000000, 2441406250, 2500000000, 3125000000, 3200000000, 3906250000, 4000000000, 4882812500, 5000000000, 6250000000, 7812500000, 8000000000, 9765625000, 10000000000, 12500000000, 15625000000, 16000000000, 19531250000, 20000000000, 25000000000, 31250000000, 39062500000, 40000000000, 50000000000, 62500000000, 78125000000, 80000000000, 100000000000, 125000000000, 156250000000, 200000000000, 250000000000, 312500000000, 400000000000, 500000000000, 625000000000, 1000000000000, 1250000000000, 2000000000000, 2500000000000, 5000000000000, 10000000000000

  • The sum of all divisors of 1013, including itself, is 24,998,474,116,998.
  • It has anEuler totient of 4,000,000,000,000, and analiquot sum of 14,998,474,116,998.
  • There are a total of 346,065,536,839 positiveprimes less than 1013.[1]
  • Below is the list of basic calculations of 10,000,000,000,000:
Multiplication
10,000,000,000,000 × x{\displaystyle \scriptstyle {{\text{10,000,000,000,000 }}\times {\text{ x}}}}
Division
10,000,000,000,000 ÷ x{\displaystyle \scriptstyle {{\text{10,000,000,000,000 }}\div {\text{ x}}}}
Exponentiation
10,000,000,000,000x{\displaystyle \scriptstyle {{\text{10,000,000,000,000}}^{\text{x}}}}
nth root

10,000,000,000,000x{\displaystyle \scriptstyle {\sqrt[{\text{x}}]{\text{10,000,000,000,000}}}}

220,000,000,000,0005,000,000,000,0001026≈3,162,277.6602
330,000,000,000,0003,333,333,333,333.31039≈21,544.3469
440,000,000,000,0002,500,000,000,0001052≈1,778.2794
550,000,000,000,0002,000,000,000,0001065≈398.1072
660,000,000,000,0001,666,666,666,666.61078≈146.7799
770,000,000,000,0001,428,571,428,571.4285711091≈71.9686
880,000,000,000,0001,250,000,000,00010104≈42.1697
990,000,000,000,0001,111,111,111,111.110117≈27.8256
10100,000,000,000,0001,000,000,000,00010130≈19.9526

In economy

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10 trillion Zimbabwean Dollars (2008)

Selected 14-digit numbers (10,000,000,000,001–99,999,999,999,999)

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10,000,000,000,001 to 19,999,999,999,999

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  • 10,000,000,000,037 : smallest 14-digitprime number[2]
  • 10,000,002,437,316 : smallest 14-digittriangular number, 4,472,136th triangular number[3][4]
  • 10,153,507,819,457 : 177thMarkov number[5]
  • 10,445,360,463,871 : 38thWoodall number[6]
  • 10,610,209,857,723 : 64thFibonacci number
  • 11,038,251,159,312 : number of 51-bead necklaces (turning over is allowed) where complements are equivalent[7]
  • 11,111,111,111,111 :repunit
  • 11,258,999,739,560 : number of 50-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[8]
  • 13,046,940,568,625 : number of series-reduced planted trees with 48 nodes[9]
  • 13,432,403,613,621 : number of secondary structures of RNA molecules with 37 nucleotides[10]
  • 13,933,569,346,707 : 32ndMotzkin number[11]
  • 13,974,537,376,800 : 75thsuperabundant number[12]
  • 14,173,019,355,266 : 178th Markov number
  • 14,235,090,298,445 : 179th Markov number
  • 14,622,039,889,385 : 180th Markov number
  • 15,988,960,048,321 : 181st Markov number
  • 17,167,680,177,565 : 65th Fibonacci number, 182nd Markov number
  • 18,367,353,072,152 : 26thCatalan number[13]
  • 18,632,716,502,400 : 76th superabundant number
  • 18,696,424,380,481 : 183rd Markov number
  • 19,374,186,136,140 : 41stWedderburn-Etherington number[14]
  • 19,696,509,177,019 : 16thalternating factorial[15]

20,000,000,000,000 to 29,999,999,999,999

[edit]
  • 20,922,789,888,000 = 16!
  • 20,922,789,888,136 : 16thfactoriangular number[16]
  • 21,246,581,423,810 : 184th Markov number
  • 21,300,003,689,580 : 36thPell number[17]
  • 21,440,476,741,631 : 39th Woodall number
  • 21,651,955,485,304 : number of 52-bead necklaces (turning over is allowed) where complements are equivalent
  • 22,076,468,764,192 : number of 51-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
  • 22,222,222,222,222 :repdigit
  • 22,592,065,572,301 : 185th Markov number
  • 24,351,056,611,103 : number of (unordered, unlabeled) rooted trimmedtrees with 39 nodes[18]
  • 26,500,373,448,281 : 186th Markov number
  • 27,673,060,569,305 : number of series-reduced planted trees with 49 nodes
  • 27,777,890,035,288 : 66th Fibonacci number
  • 27,949,074,753,600 : 77th superabundant number

30,000,000,000,000 to 39,999,999,999,999

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  • 30,901,824,368,813 : 187th Markov number
  • 31,801,503,090,601 : 188th Markov number
  • 32,607,253,879,200 : 78th superabundant number
  • 33,333,333,333,333 : repdigit
  • 33,843,022,209,066 : number of secondary structures of RNA molecules with 38 nucleotides
  • 36,332,699,889,481 : 189th Markov number
  • 38,596,477,083,550 : number of square (0,1)-matrices without zero rows and with exactly 12 entries equal to 1[19]

40,000,000,000,000 to 49,999,999,999,999

[edit]
  • 40,002,464,776,083 : 33rd Motzkin number
  • 40,081,787,109,376 : 25thautomorphic number[20]
  • 42,486,822,491,890 : number of 53-bead necklaces (turning over is allowed) where complements are equivalent
  • 43,303,843,861,744 : number of 52-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
  • 43,520,999,798,747 : 50threpfigit[21]
  • 43,980,465,111,039 : 40th Woodall number
  • 44,444,444,444,444 : repdigit
  • 44,945,570,212,853 : 67th Fibonacci number, 190th Markov number
  • 46,127,828,641,049 : 191st Markov number
  • 46,384,328,517,112 : 42nd Wedderburn-Etherington number
  • 47,574,827,600,981 : 21stSchröder–Hipparchus number[22]
  • 48,795,987,025,021 : 192nd Markov number

50,000,000,000,000 to 59,999,999,999,999

[edit]
  • 51,011,754,393,600 = 26!!
  • 51,422,757,785,981 : 37th Pell number, 193rd Markov number
  • 55,555,555,555,555 : repdigit
  • 55,898,149,507,200 : 79th superabundant number
  • 57,850,602,535,042 : 194th Markov number
  • 58,734,306,828,191 : number of series-reduced planted trees with 50 nodes
  • 59,918,212,890,625 : 26th automorphic number

60,000,000,000,000 to 69,999,999,999,999

[edit]
  • 60,941,642,779,903 : number of (unordered, unlabeled) rooted trimmed trees with 40 nodes
  • 65,082,055,350,517 : 195th Markov number
  • 65,214,507,758,400 : 80th superabundant number, 19thsuperior highly composite number[23]
  • 66,666,666,666,666 : repdigit
  • 67,082,333,460,610 : 196th Markov number
  • 68,275,077,901,156 : number ofposets with 15 unlabeled elements[24]
  • 69,533,550,916,004 : 27th Catalan number

70,000,000,000,000 to 79,999,999,999,999

[edit]
  • 72,723,460,248,141 : 68th Fibonacci number
  • 73,224,462,646,361 : 197th Markov number
  • 74,596,893,730,427 : 51th repfigit
  • 77,777,777,777,777 : repdigit

80,000,000,000,000 to 89,999,999,999,999

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  • 80,902,026,460,669 : 198th Markov number
  • 82,561,235,448,866 : 199th Markov number
  • 83,400,061,453,514 : number of 54-bead necklaces (turning over is allowed) where complements are equivalent
  • 84,973,577,874,916 : number of 53-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
  • 85,349,327,734,485 : number of secondary structures of RNA molecules with 39 nucleotides
  • 88,888,888,888,888 : repdigit

90,000,000,000,000 to 99,999,999,999,999

[edit]
  • 90,159,953,477,631 : 41st Woodall number
  • 93,139,301,545,921 : 200th Markov number
  • 97,295,849,958,669 : 52nd repfigit
  • 97,568,760,404,309 : 201st Markov number
  • 97,821,761,637,600 : 81st superabundant number
  • 99,999,999,999,973 : largest 14-digit prime number[25]
  • 99,999,999,999,999 : largest 14-digit number, repdigit

See also

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References

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  1. ^Sloane, N. J. A. (ed.)."Sequence A006880 (Number of primes less than 10^n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^Sloane, N. J. A. (ed.)."Sequence A003617 (Smallest n-digit prime)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^Sloane, N. J. A. (ed.)."Sequence A068093 (Smallest n-digit triangular number)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^Sloane, N. J. A. (ed.)."Sequence A068092 (Index of smallest triangular number with n digits)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^Sloane, N. J. A. (ed.)."Sequence A002559 (Markoff (or Markov) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^Sloane, N. J. A. (ed.)."Sequence A003261 (Woodall (or Riesel) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^Sloane, N. J. A. (ed.)."Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^Sloane, N. J. A. (ed.)."Sequence A000013 (Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^Sloane, N. J. A. (ed.)."Sequence A001678 (Number of series-reduced planted trees with n nodes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^Sloane, N. J. A. (ed.)."Sequence A004148 (Generalized Catalan numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^Sloane, N. J. A. (ed.)."Sequence A001006 (Motzkin numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. ^Sloane, N. J. A. (ed.)."Sequence A004394 (Superabundant [or super-abundant] numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ^Sloane, N. J. A. (ed.)."Sequence A000108 (Catalan numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ^Sloane, N. J. A. (ed.)."Sequence A001190 (Wedderburn-Etherington numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  15. ^Sloane, N. J. A. (ed.)."Sequence A005165 (Alternating factorials)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ^Sloane, N. J. A. (ed.)."Sequence A101292".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  17. ^Sloane, N. J. A. (ed.)."Sequence A000129 (Pell numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ^Sloane, N. J. A. (ed.)."Sequence A002955 (Number of (unordered, unlabeled) rooted trimmed trees with n nodes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  19. ^Sloane, N. J. A. (ed.)."Sequence A122400 (Number of square (0,1)-matrices without zero rows and with exactly n entries equal to 1)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. ^Sloane, N. J. A. (ed.)."Sequence A003226 (Automorphic numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^Sloane, N. J. A. (ed.)."Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  22. ^Sloane, N. J. A. (ed.)."Sequence A001003 (Schroeder's second problem (generalized parentheses))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  23. ^Sloane, N. J. A. (ed.)."Sequence A002201 (Superior highly composite numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  24. ^Sloane, N. J. A. (ed.)."Sequence A000112 (Number of partially ordered sets ("posets") with n unlabeled elements)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  25. ^Sloane, N. J. A. (ed.)."Sequence A003618 (Largest n-digit prime)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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