Number 999

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[Library]  First 3 digits in Dewey Decimal Classification System call number for library books in Extraterrestrial Worlds.

[Math.]  Its odd powers end with 999. Its even powers end with 001.

[Math.]  9992 = 998,001 = (998+001)2

9993 = 997,002,999 = (997+002)2

[Math.]

1113 = 1,367,631 = (1+367+631)3

2223 = 10,941,048 = (10+941+048)3

3333 = 36,926,037 = (36+926+037)3

4443 = 87,528,384 = (87+528+384)3

6663 = 295,408,296 = (295+408+296)3

7773 = 469,097,433 = (469+097+433)3

8883 = 700,227,072 = (700+227+072)3

5553 = 170,953,875 and 170+953+875 = 2×999

9993 = 997,002,999 and 997+002+999 = 2×999.

[Math.]

111,1113 =   1,371,737,997,260,631 and 1+371+737+997+260+631 = 3×999

222,2223 = 10,973,903,978,085,048 and 10+973+903+978+085+048 = 3×999

333,3333 = 37,036,925,926,037,037 and 37+036+925+926+037+037 = 2×999

444,4443 = 87,791,231,824,680,384 and 87+791+231+824+680+384 = 3×999

555,5553 = 171,467,249,657,578,875 and 171+467+249+657+578+875 = 3×999

666,6663 = 296,295,407,408,296,296 and 296+295+407+408+296+296 = 2×999

777,7773 = 470,506,133,060,396,433 and 470+506+133+060+396+433 = 2×999

888,8883 = 702,329,854,597,443,072 and 702+329+854+597+443+072 = 3×999

999,9993 = 999,997,000,002,999,999 and 999+997+000+002+999+999 = 4×999.

[Math.]  (Sum of 2 root numbers on each row is 999, i.e. 232+767 = 999...)

2322 = 053,824 & 053+824 = 877 & 7672 = 588,289 & 588+289 = 877

2122 = 044,944 & 044+944 = 988 & 7872 = 619,369 & 619+369 = 988

4542 = 206,116 & 206+116 = 322 & 5452 = 297,025 & 297+025 = 322

4342 = 188,356 & 188+356 = 544 & 5652 = 319,225 & 319+225 = 544

3432 = 117,649 & 117+649 = 766 & 6562 = 430,336 & 430+336 = 766

3232 = 104,329 & 104+329 = 433 & 6762 = 456,976 & 456+976 = 1432 & 1+432 = 433

1212 = 014,641 & 014+641 = 655 & 8782 = 770,884 & 770+884 = 1654 & 1+654 = 655

1012 = 010,201 & 010+201 = 211 & 8982 = 806,404 & 806+404 = 1210 & 1+210 = 211.

[Math.]

The 6-digit period of the rational number 1/13 = 0.076923076923… or 0.076923. Its multiple by 13 is 999,999.  Then,   076,923×n = abc,def,ghi,jkl and

 abc,def+ghi,jkl = 076,923, if n  = 13t+1 abc,def+ghi,jkl = 692,307, if n  = 13t+9 abc,def+ghi,jkl = 230,769, if n  = 13t+3 abc,def+ghi,jkl = 769,230, if n  = 13t+10 abc,def+ghi,jkl = 307,692, if n  = 13t+4 abc,def+ghi,jkl = 923,076, if n  = 13t+12

for t = 0 to 76,922, and in fact abc,edf = t.  The results are digit-rotations of 076,923.

And 076,923×n = abc,def,ghi,jkl &

 abc,def+ghi,jkl = 153,846, if n  = 13t+2 abc,def+ghi,jkl = 538,461, if n  = 13t+7 abc,def+ghi,jkl = 384,615, if n  = 13t+5 abc,def+ghi,jkl = 615,384, if n  = 13t+8 abc,def+ghi,jkl = 461,538, if n  = 13t+6 abc,def+ghi,jkl = 846,153, if n  = 13t+11

for t = 0 to 76,922, and in fact abc,edf = t.  The results are digit-rotations of 076,923×2 = 153,846. It is the period of the rational number 2/13 = 0.153846153846… or 0.153846), and the sums of first and last 3-digit numbers are always 999.

[Math.]  The 6-digit period of the rational number 1/7 = 0.142857142857… or 0.142857. Its multiple by 7 is 999,999.  Then,             142,857×n = abc,def,ghi,jkl and

 abc,def+ghi,jkl = 142,857, if n  = 7t+1 abc,def+ghi,jkl = 571,428, if n  = 7t+4 abc,def+ghi,jkl = 285,714, if n  = 7t+2 abc,def+ghi,jkl = 714,285, if n  = 7t+5 abc,def+ghi,jkl = 428,571, if n  = 7t+3 abc,def+ghi,jkl = 857,142, if n  = 7t+6,

for t = 0 to 142,856, and in fact abc,edf = t. The results are digit-rotations of 142,857 and the sums of first and last 3-digit numbers are always 999.

[Math.]

(343+656 = 999 = 323+676)

3432 = 117,649 & 117+649 = 766

6562 = 430,336 & 430+336 = 766

3232 = 104,329 & 104+329 = 433

6762 = 456,976 & 456+976 = 1432  and 1+432 = 433.

(232+767 = 999 = 212+787)

2322 = 053,824 & 053+824 = 877

7672 = 588,289 & 588+289 = 877

and

2122 = 044,944 & 044+944 = 988

7872 = 619,369 & 619+369 = 988.

(454+545 = 999 = 434+565)

4542 = 206,116 & 206+116 = 322

5452 = 297,025 & 297+025 = 322

and

4342 = 188,356 & 188+356 = 544

5652 = 319,225 & 319+225 = 544

(121+878 = 999 = 101+898)

1212 = 014,641 & 014+641 = 655

8782 = 770,884 & 770+884 = 1654 and 1+654 = 655.

and

1012 = 010,201 & 010+201 = 211

8982 = 806,404 & 806+404 = 1210 and 1+210 = 211.

[Phone]  The emergency telephone number dialing within the United Kingdom, Poland, Zambia, Uganda, Tanzania, Burma (Myanmar), Brunei, Hong Kong, Macau, Kenya, Samoa, Western Samoa, Oman, Seychelles, Uganda and Ireland.

[Phone]   The emergency telephone numbers dialing within Qatar are 999 and 118.

[Phone]  The emergency telephone numbers dialing within United Arab Emirates (Abu Dhabi) are 999 and 998.

[Phone]   The emergency telephone numbers dialing within Montserrat and Uruguay are 999 and 911.

[Phone]  The emergency telephone numbers dialing within Trinidad and Tobago are 999 and 990.

[Phone] The emergency telephone numbers dialing within Singapore are 999 and 995.

[Phone]   The emergency telephone numbers dialing within Malaysia  are 999 and 994.

[Phone]   The number to key in text messaging on telephone keypad for letter Y.

[Trivia]  The largest 3-digit number or the maximum number that can be displayed by a 3-digit counter.

900-999

[Library]  Numbers 900-999 are the first 3 digits in Dewey Decimal Classification System call numbers for library books in History and Geography.