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For a 32-bit "single-precision" floating point number, we have 24 (23 stored + 1 implicit) of these mantissa bits to work with. That means in the range \$[2^n, 2^{n+1})\$ we have \$2^{24}\$ representable numbers, spaced \$2^{n-24}\$ apart.

If we try to store a number that falls between two representable numbers, it gets rounded to the nearest one, making an error of up to \$2^{n-25}\$. That could, for example, nudge an object or vertex or camera position a little to the left or to the right of where it's supposed to be. This answer includes a table of what relative precision we have at various ranges from the origin.

For a 32-bit "single-precision" floating point number, we have 24 (23 stored + 1 implicit) of these mantissa bits to work with. That means in the range \$[2^n, 2^{n+1})\$ we have \$2^{23}\$ representable numbers, spaced \$2^{n-23}\$ apart.

If we try to store a number that falls between two representable numbers, it gets rounded to the nearest one, making an error of up to \$2^{n-24}\$. That could, for example, nudge an object or vertex or camera position a little to the left or to the right of where it's supposed to be. This answer includes a table of what relative precision we have at various ranges from the origin.

For a 32-bit "single-precision" floating point number, we have 23 of these mantissa bits to work with. That means in the range \$[2^n, 2^{n+1})\$ we have \$2^{23}\$ representable numbers, spaced \$2^{n-23}\$ apart.

If we try to store a number that falls between two representable numbers, it gets rounded to the nearest one, making an error of up to \$2^{n-24}\$. That could, for example, nudge an object or vertex or camera position a little to the left or to the right of where it's supposed to be. This answer includes a table of what relative precision we have at various ranges from the origin.

For a 32-bit "single-precision" floating point number, we have 24 (23 stored + 1 implicit) of these mantissa bits to work with. That means in the range \$[2^n, 2^{n+1})\$ we have \$2^{24}\$ representable numbers, spaced \$2^{n-24}\$ apart.

If we try to store a number that falls between two representable numbers, it gets rounded to the nearest one, making an error of up to \$2^{n-25}\$. That could, for example, nudge an object or vertex or camera position a little to the left or to the right of where it's supposed to be. This answer includes a table of what relative precision we have at various ranges from the origin.

Once we lose that precision in a calculation, we don't get it back if we later bring the result back closer to the origin - there are no bits left to encode that lost high-precision information, so it's not visible to any calculations downstream. This precision loss can snowball through repeated calculations, if we round a number, then use the rounded result to make a new number that also get rounded...

Once we lose that precision in a calculation, we don't get it back if we later bring the result back closer to the origin - there are no bits left to encode that lost high-precision information, so it's not visible to any calculations downstream. This precision loss can snowball through repeated calculations, if we round a number, then use the rounded result to make a new number that also gets rounded...

See a high-res version of this visualization rendered in WebGL here