a=40.0 plus-minus 0.1 cm (uncertainty)

b=2.5 plus-minus 0.05 cm (uncertainty)

Find a/b and its uncertainty

Is it 16cm plus-minus 1cm of uncertainty

or is it 16.0cm plus-minus 0.4 cm of uncertainty

multiplying or dividing

...add the percent uncertainties

16 ± 2.25%

the cm are cancelled in the division process...it's just a ratio

To find the value of a/b and its uncertainty, we can use the concept of relative uncertainties. The relative uncertainty is calculated by taking the ratio of the individual uncertainties to their corresponding values. Let's calculate it step by step.

Given:
a = 40.0 ± 0.1 cm
b = 2.5 ± 0.05 cm

1. Calculate a/b:
To find the value of a/b, divide the values of a and b:
a/b = 40.0 cm / 2.5 cm = 16.0

2. Calculate the relative uncertainty:
To determine the uncertainty of a/b, we need to calculate the relative uncertainty. The relative uncertainty is obtained by dividing the uncertainty of a/b by the value of a/b:
Relative uncertainty = (uncertainty of a/b) / (a/b)

For a/b = 16.0, we need to calculate how the uncertainty of a/b changes:
Uncertainty of a/b = (relative uncertainty of a) + (relative uncertainty of b)

a. Calculate the relative uncertainty of a:
Relative uncertainty of a = (uncertainty of a) / (a) = 0.1 cm / 40.0 cm = 0.0025

b. Calculate the relative uncertainty of b:
Relative uncertainty of b = (uncertainty of b) / (b) = 0.05 cm / 2.5 cm = 0.02

3. Calculate the total relative uncertainty:
Total relative uncertainty = (0.0025) + (0.02) = 0.0225

4. Calculate the uncertainty of a/b:
Uncertainty of a/b = (Total relative uncertainty) * (a/b) = 0.0225 * 16.0 = 0.36 cm

Therefore, the value of a/b is 16.0 cm, and its uncertainty is ± 0.36 cm.

Hence, the correct answer is 16.0 cm plus-minus 0.36 cm of uncertainty.