Relative Time Rounding2.14.0+

moment.relativeTimeRounding();  // getter
moment.relativeTimeRounding(fn);  // setter

duration.humanize rounds a possibly double value before supplying it to the relativeTime format string specified in the locale. To control the rounding you can use moment.relativeTimeRounding.

var roundingDefault = moment.relativeTimeRounding();
// Round relative time evaluation down
moment.relativeTimeRounding(Math.floor);
moment.relativeTimeThreshold('s', 60);
moment.relativeTimeThreshold('m', 60);
moment.relativeTimeThreshold('h', 24);
moment.relativeTimeThreshold('d', 31);
moment.relativeTimeThreshold('M', 12);
var a = moment();
a.subtract({hours: 23, minutes: 59, seconds: 59});
a.toNow()  // == 'in 23 hours'  'Round down towards the nearest hour'
// back to default
moment.relativeTimeRounding(roundingDefault);

You can even choose to do no rounding at all:

var retainValue = function (value) {
    return value;
};
moment.relativeTimeRounding(retainValue);
var a = moment();
a.subtract({hours: 39});
a.toNow() // == 'in 1.625 days', 'Round down towards the nearest year'