Rounding to the Nearest Hundered-Thousandths

var num = 89500;var rounded = -Math.round(-num / 1000) * 1000;console.log('rounding tie down: ', rounded);  // 89000

var num = 89500;var rounded = Math.round(num / 1000) * 1000;console.log('rounding tie up: ', rounded);  // 90000

Efficient way of finding the number of decimals a double value has

If you want a solution that will tell you that information in a way that will agree with the eventual result of converting the double to a string, then efficiency doesn't really come into it; you basically have to convert to string and check. The result is that it's entirely possible for a double to contain a value that mathematically has a (say) non-zero value in (say) the hundred-thousandth place, but which when converted to string will not. Such is the joy of IEEE-754 double-precision binary floating point: The number of digits you get from the string representation is only as many as necessary to distinguish the value from its adjacent representable value. From the Double docs:

How many digits must be printed for the fractional part of m or a? There must be at least one digit to represent the fractional part, and beyond that as many, but only as many, more digits as are needed to uniquely distinguish the argument value from adjacent values of type double. That is, suppose that x is the exact mathematical value represented by the decimal representation produced by this method for a finite nonzero argument d. Then d must be the double value nearest to x; or if two double values are equally close to x, then d must be one of them and the least significant bit of the significand of d must be 0.

But if you're not concerned about that, and assuming limiting your value range to long is okay, you can do something like this:

private static boolean onlyThreePlaces(double v) {
    double d = (double)((long)(v * 1000)) / 1000;
    return d == v;
}

...which should have less memory overhead than a String-round-trip.

However, I'd be surprised if there weren't a fair number of times when that method and the result of Double.toString(double) didn't match in terms of digits after the decimal, for the reasons given above.

In a comment on the question, you've said (when I asked about the value range):

Honestly I'm not sure. I'm dealing with prices; For starters, I'll assume 0-200K

Using double for financial values is usually not a good idea. If you don't want to use BigDecimal because of memory concerns, pick your precision and use int or long depending on your value range. For instance, if you only need to-the-penny precision, you'd use values multiplied by 100 (e.g., 2000 is Ⓠ20 [or whatever currency you're using, I'm using Ⓠ for quatloos]). If you need precision to thousanths of a penny (as your question suggests), then multiply by 100000 (e.g., 2000000 is Ⓠ20). If you need more precision, pick a larger multiplier. Even if you go to hundred-thousanths of a penny (muliplier: 10000000), with long you have a range of Ⓠ-922,337,203,685 to Ⓠ922,337,203,685.

This has the side-benefit that it makes this check easier: Just a straight %. If your multiplier is 10000000 (hundred-thousandths of a penny), it's just value % 10000 != 0 to identify invalid ones (or value % 10000 == 0 to identify valid ones).

long num1 = 100120000;  // 10.012   => true
                        // 100120000 % 10000 is 0 = valid
long num2 = 102211000;  // 10.2211  => false
                        // 102211000 % 10000 is 1000 = invalid
long num3 = 102000000;  // 10.2     => true
                        // 102000000 % 10000 is 0 = valid

Why does the floating-point value of 4*0.1 look nice in Python 3 but 3*0.1 doesn't?

The simple answer is because 3*0.1 != 0.3 due to quantization (roundoff) error (whereas 4*0.1 == 0.4 because multiplying by a power of two is usually an "exact" operation). Python tries to find the shortest string that would round to the desired value, so it can display 4*0.1 as 0.4 as these are equal, but it cannot display 3*0.1 as 0.3 because these are not equal.

You can use the .hex method in Python to view the internal representation of a number (basically, the exact binary floating point value, rather than the base-10 approximation). This can help to explain what's going on under the hood.

>>> (0.1).hex()
'0x1.999999999999ap-4'
>>> (0.3).hex()
'0x1.3333333333333p-2'
>>> (0.1*3).hex()
'0x1.3333333333334p-2'
>>> (0.4).hex()
'0x1.999999999999ap-2'
>>> (0.1*4).hex()
'0x1.999999999999ap-2'

0.1 is 0x1.999999999999a times 2^-4. The "a" at the end means the digit 10 - in other words, 0.1 in binary floating point is very slightly larger than the "exact" value of 0.1 (because the final 0x0.99 is rounded up to 0x0.a). When you multiply this by 4, a power of two, the exponent shifts up (from 2^-4 to 2^-2) but the number is otherwise unchanged, so 4*0.1 == 0.4.

However, when you multiply by 3, the tiny little difference between 0x0.99 and 0x0.a0 (0x0.07) magnifies into a 0x0.15 error, which shows up as a one-digit error in the last position. This causes 0.1*3 to be very slightly larger than the rounded value of 0.3.

Python 3's float repr is designed to be round-trippable, that is, the value shown should be exactly convertible into the original value (float(repr(f)) == f for all floats f). Therefore, it cannot display 0.3 and 0.1*3 exactly the same way, or the two different numbers would end up the same after round-tripping. Consequently, Python 3's repr engine chooses to display one with a slight apparent error.

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