Almost integers

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Almost integers (or near integers) are numbers which, although not being integers on account of having a fractional part, are very close to integers and can be mistaken for such as the result of a loss of machine precision during a calculation. For example, 99.99999999999 is an almost integer that is almost the integer 100.

Ramanujan's constant

Ramanujan's constant is amazingly close to an integer, the first 12 digits after the decimal point being 9. The decimal expansion of Ramanujan's constant is

$e^{\pi {\sqrt {163}}}=262537412640768743.9999999999992500725971981856888793538563373369908627075374103782\ldots \,$

A060295 Decimal expansion of e^(Pi*sqrt(163)).

{2, 6, 2, 5, 3, 7, 4, 1, 2, 6, 4, 0, 7, 6, 8, 7, 4, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 5, 0, 0, 7, 2, 5, 9, 7, 1, 9, 8, 1, 8, 5, 6, 8, 8, 8, 7, 9, 3, 5, 3, 8, 5, 6, 3, 3, 7, 3, 3, 6, 9, 9, 0, 8, 6, 2, 7, 0, 7, 5, 3, 7, 4, 1, 0, ...}

Pi^3

Pi^3 is somewhat close to an integer, the first 2 digits after the decimal point being 0. The decimal expansion of $\scriptstyle \pi ^{3}\,$ is

$\pi ^{3}=31.00627668029982017547631506710139520222528856588510769414453810380639\ldots \,$

A091925 Decimal expansion of pi^3.

{3, 1, 0, 0, 6, 2, 7, 6, 6, 8, 0, 2, 9, 9, 8, 2, 0, 1, 7, 5, 4, 7, 6, 3, 1, 5, 0, 6, 7, 1, 0, 1, 3, 9, 5, 2, 0, 2, 2, 2, 5, 2, 8, 8, 5, 6, 5, 8, 8, 5, 1, 0, 7, 6, 9, 4, 1, 4, 4, 5, 3, 8, 1, 0, 3, 8, 0, 6, 3, 9, 4, 9, 1, 7, 4, 6, 5, 7, ...}

Also, observe that the decimal expansion of $\scriptstyle \pi ^{3}-31\,$ is nearly

${\frac {2\pi }{10^{3}}}=0.0062831853071\ldots \,$