Question

What is the range of lengths for 50-m pools that have an uncertainty of ± 10 cm? ±1 cm? ± 1 mm? (For example, if the uncertainty of the pool were ± 1 m, the range of lengths would be 49–51 m.)

Answer 1

1. For uncertainty of ± 10 cm.

The lengths of pools are $50m = 5000cm$. Thus, the range is

$$(5000cm-10cm)-(5000cm+10cm)\\ 4990-5010cm$$

2. For uncertainty of ± 1 cm.

The range is:

$$(5000cm-1cm)-(5000cm+1cm)\\ 4999-5001cm$$

3. For uncertainty of ± 1 mm.

The lengths of pools are $50m = 5000cm = 50000mm$. The range is:

$$(50000mm-1mm)-(5000mm+1mm)\\ 49999-50001mm$$

Answer. $4990-5010cm$, $4999-5001cm$ and $49999-50001mm$ respectively.