How to do it...

The following steps show you how to quantify uncertainty on numerical values in calculations:

1. First, we create an uncertain float value of 3.0 plus or minus 0.4:

seconds = ufloat(3.0, 0.4)
print(seconds)  # 3.0+/-0.4

2. Next, we perform a calculation involving this uncertain value to obtain a new uncertain value:

depth = 0.5*9.81*seconds*seconds
print(depth)  # 44+/-12

3. Next, we create a new uncertain float value and apply the sqrt routine from the umath module in the reverse of the previous calculation:

other_depth = ufloat(44, 12)
time = umath.sqrt(2.0*other_depth/9.81)
print("Estimated time", time)
# Estimated time 3.0+/-0.4