Incorrect result in numbers
ROUNDDOWN(1,0231;4) = 1,023 (incorrect)
ROUNDDOWN(1,0232;4) = 1,0232 (correct)
MacBook, OS X Mavericks (10.9.2)
Maybe...
Overall I think this may be a problem with how numbers are stored internally.
Here's why... The value (column A) ranges from values that start before the number you noticed as "weird" (1.0231) and goes after. Column C uses the formula rounddown(A, 4), and column B computes the absolute value of the error between the two.
Value | Error | Rounded Down (4 places) |
1.0195 | 0.0001 | 1.0194 |
1.0196 | 0.0001 | 1.0195 |
1.0197 | 0.0001 | 1.0196 |
1.0198 | 0.0001 | 1.0197 |
1.0199 | 0.0001 | 1.0198 |
1.0200 | 0.0001 | 1.0199 |
1.0201 | 0.0001 | 1.0200 |
1.0202 | 0.0001 | 1.0201 |
1.0203 | 0.0001 | 1.0202 |
1.0204 | 0.0001 | 1.0203 |
1.0205 | 0.0001 | 1.0204 |
1.0206 | 0.0001 | 1.0205 |
1.0207 | 0.0001 | 1.0206 |
1.0208 | 0.0001 | 1.0207 |
1.0209 | 0.0001 | 1.0208 |
1.0210 | 0.0001 | 1.0209 |
1.0211 | 0.0001 | 1.0210 |
1.0212 | 0.0001 | 1.0211 |
1.0213 | 0.0001 | 1.0212 |
1.0214 | 0.0001 | 1.0213 |
1.0215 | 0.0001 | 1.0214 |
1.0216 | 0.0001 | 1.0215 |
1.0217 | 0.0001 | 1.0216 |
1.0218 | 0.0001 | 1.0217 |
1.0219 | 0.0001 | 1.0218 |
1.0220 | 0.0001 | 1.0219 |
1.0221 | 0.0001 | 1.0220 |
1.0222 | 0.0001 | 1.0221 |
1.0223 | 0.0001 | 1.0222 |
1.0224 | 0.0001 | 1.0223 |
1.0225 | 0.0001 | 1.0224 |
1.0226 | 0.0001 | 1.0225 |
1.0227 | 0.0001 | 1.0226 |
1.0228 | 0.0001 | 1.0227 |
1.0229 | 0.0001 | 1.0228 |
1.0230 | 0.0001 | 1.0229 |
1.0231 | 0.0001 | 1.0230 |
1.0232 | 0.0000 | 1.0232 |
1.0233 | 0.0000 | 1.0233 |
1.0234 | 0.0000 | 1.0234 |
1.0235 | 0.0000 | 1.0235 |
1.0236 | 0.0000 | 1.0236 |
1.0237 | 0.0000 | 1.0237 |
1.0238 | 0.0000 | 1.0238 |
1.0239 | 0.0000 | 1.0239 |
1.0240 | 0.0000 | 1.0240 |
1.0241 | 0.0000 | 1.0241 |
1.0242 | 0.0000 | 1.0242 |
1.0243 | 0.0000 | 1.0243 |
1.0244 | 0.0000 | 1.0244 |
1.0245 | 0.0000 | 1.0245 |
1.0246 | 0.0000 | 1.0246 |
1.0247 | 0.0000 | 1.0247 |
1.0248 | 0.0000 | 1.0248 |
1.0249 | 0.0000 | 1.0249 |
1.0250 | 0.0000 | 1.0250 |
1.0251 | 0.0000 | 1.0251 |
1.0252 | 0.0000 | 1.0252 |
1.0253 | 0.0000 | 1.0253 |
1.0254 | 0.0000 | 1.0254 |
1.0255 | 0.0000 | 1.0255 |
1.0256 | 0.0000 | 1.0256 |
1.0257 | 0.0000 | 1.0257 |
1.0258 | 0.0000 | 1.0258 |
1.0259 | 0.0000 | 1.0259 |
1.0260 | 0.0000 | 1.0260 |
1.0261 | 0.0000 | 1.0261 |
1.0262 | 0.0000 | 1.0262 |
1.0263 | 0.0000 | 1.0263 |
1.0264 | 0.0000 | 1.0264 |
Rounddown should tend towards zero. That is, the result should always be the same, or closer, to zero. I think, like you, that the vlues you are using with the number of digits should produce the same value. There maybe a reason they do not.
the number 1024 is a power of two, so (1024 - 1)/1000 may be one of those numbers that is imperfect when stored in a limited precision digital number.
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