Numbers 900,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

900,000,000 –  910,000,000920,000,000930,000,000 – 940,000,000

[1M] & [10M] &
[100M- [200M] - [300M] - [400M] - [500M] - [600M] - [700M] - [800M] - [900M]  & [1B]

1  - 10 - 100  - 1000 - 10,000 - 100,000 - 1M - 10M - 100M1B10B - 100B - 1T - 10T - 100T - 1Q ...

900,000,007

[Math.]

1×8+1 = 9

12×8+2 = 98

123×8+3 = 987

1,234×8+4 = 9,876

12,345×8+5 = 98,765

123,456×8+6 = 987,654

1,234,567×8+7 = 9,876,543

12,345,678×8+8 = 98,765,432

123,456,789×8+9 = 987,654,321

1,234,567,890×8+90 = 9,876,543,210

(start of a new cycle)

12,345,678,901×8+901 = 98,765,432,109

123,456,789,012×8+9,002 = 987,654,321,098

1,234,567,890,123×8+90,003 = 9,876,543,210,987

12,345,678,901,234×8+900,004 = 98,765,432,109,876

123,456,789,012,345×8+9,000,005 = 987,654,321,098,765

1,234,567,890,123,456×8+90,000,006 = 9,876,543,210,987,654

12,345,678,901,234,567×8+900,000,007 = 98,765,432,109,876,543

123,456,789,012,345,678×8+9,000,000,008 = 987,654,321,098,765,432

1,234,567,890,123,456,789×8+90000000009 = 9,876,543,210,987,654,321

12,345,678,901,234,567,890×8+ 900000000090 = 98,765,432,109,876,543,210

... (end of cycle) ...

901,234,567

[Math.]  012345679 is the 9-digit period of the rational number 1/81 = 0.012345679012345679… or 0.012,345,679.

Multiples of 012345679 by 1, 10, 19, 28, 37, 46, 55, 64 and 73 yield all 9 digit-rotations of the number itself: 012,345,679, 123,456,790, 234,567,901, 345,679,012, 456,790,123, 567,901,234, 679,012,345, 790,123,456 and 901,234,567. All numbers are missing digit 8.

Multiples of 012345679 by a number from 1 to 80 of the form x (mod 9), where x = 1, 2, 4, 5, 7 or 8, will yield a 9-digit number, including all but one digit from 0 to 9. The missing digit is (9–x), again taking only values: 8, 7, 5, 4, 2 or 1. (Adding extra 0 to any 8-digit numbers). Its multiple by 81 is 999,999,999.

908,118,225

[Math.] Sum of the first 245 cube numbers:

13+23+…+2453 = 908,118,225 = (1+2+…+245)2 = 30,1352.

908,714,352

[Math.] 908,714,3523 =  750,381,574,940,393,412,517,982,208; All digits are “triplicated”. (References [15])

xyz,abc,def

[Math.]  For any xyz = 100 to 999, there are always six 6-digit numbers abc,edf such that the sum (xyz+abc,def) is equal to one of 6 digit-rotations of 142,857 and the number  xyz,abc,def is a multiple of 142,857.

For any xyz = 100 to 999, there are always twelve 6-digit numbers abc,edf such that the sum (xyz+abc,def) is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number xyz,abc,def is a multiple of 76,923

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References [15]