3.2 Practice problems

1. Round the following numbers:
   1. 37.7°C (to the nearest degree)
   2. 121 mM (to the nearest 10 mM)
   3. 505.3 g (to the nearest 100 g)
   4. 505.3 g (to the nearest 10 g)
   5. 14.5 g l^–1 (to the nearest g l^–1)
   6. 0.0245 g (to the nearest mg)
   7. 1.456 µg (to the nearest 100 ng)
2. Practice estimating the answers to the following calculations in your head. Then compare your answer to a precise calculation.

1. 1. 920 × 27 =
   2. 8,453 ÷ 53 =
   3. 79 × 91 =
   4. 1,205 × 0.76 =
   5. 4,215 – 2,498 =

Solution to Practice Problem 3.2a.

Back of the envelope calculations

Sometimes you might hear these kind of calculations as ‘back of the envelope’ or ‘back of the napkin’ calculations. This is meant to emphasise that they are based on rough estimates. However, these kinds of calculations can be useful, particularly when assessing if an experimental approach may be feasible or as a sanity check when assessing data. Even though a rough estimate may be crude, it is often enough to know the relevant order of magnitude of a value.

To do these sorts of calculations you need to be confident with units, SI prefixes and working with indices. These are all incredibly useful skills.

For the next ‘boffin’ question, have a go at using the estimates to work out how many proteins are in a HeLa cell. HeLa cells are a human-derived cell line commonly used for preliminary research.