Uncertainity, or margin of error, describes the imperfect nature of a measurement. Typically, it is the standard deviation of actual measurements.
Defining
According to NIST, the mass of a neutron is 1.674 927 471 x 10⁻²⁷ kg
with a standard uncertainity of 0.000 000 021 x 10⁻²⁷ kg
.
An uncertain number has a value and an uncertainty. It can be created in the following ways:
let mn = isq('1.674 927 471(21) × 10⁻²⁷ kg')
let mn = isq('1.674 927 471(21) * 10^-27 kg')
let mn = isq.unit.kg.times(isq.Number(1.674927471e-27, 0.000000021e-27))
Propagation
Anytime a calculation is performed, propagation of uncertainity is also performed to determine the uncertainty of the result.
let a = isq('1.2(2) cm'), // 1.2±0.2 cm
b = isq('1.3(3) cm'), // 1.3±0.3 cm
length = a.plus(b); // 2.5±0.4 cm
Comparision
Equality requires taking the uncertainity of both values into consideration.
ISQ defines equality as Is the difference of the two values within the resulting uncertainty?
function equals(a, b) {
let D = a.minus(b);
return D.value.abs().lte(D.uncertainty);
};