A calculator displays a result as 1.3540980 107 kg. the estimated uncertainty in the result is ±2%. how many digits should be included as significant when the result is written down?

2 significant digits.

Let's see what the range of possible values you can have for 1.3540980 if your uncertainty is + / - 2% 2% of 1.3540980 = 0.02 * 1.3540980 = 0.027082 So the lowest possible value for your result is 1.3540980 - 0.027082 = 1.327016 The largest possible result is 1.3540980 + 0.027082 = 1.38117996 Notice that only the 1st 2 digits of the result match which is reasonable since a 2% error means that your result is only accurate to within 1 part in 50.