## Learning how to use upper and lower bounds can be very important – particularly in manufacturing…

.. although they tend to be called ‘tolerances’ and are not always related to just measurements.

For example ‘high tech’ manufacturers need to work within very tight tolerances:

- On a Boeing 747 the jet engine turbine blades spin at upto 3500 revs per minute – 60 times every second. Every blade is made to a precise specification.
- A chip in a mobile phone is manufactured in a ‘clean room’ that can be 800 to a 1000 times cleaner than a hospital operating theatre. Even the smallest spec can cause the silicon to be spoiled. The ‘bounds’ of a clean room can be very tight!

The example given in the video talks about Sarah running a marathon – it’s not really ‘high tech’ but the principles are the same.

The question is a GCSE A grade:

“Sarah uses this formula to work out her average speed for a marathon.

Average speed = Distance (d) / Time (t)

d = 26.2 miles correct to 3 significant figures

t = 3.1 hours correct to 1 decimal place

Calculate the least possible value for Sarah’s average speed, Give your answer correct to 2 decimal places.”

#### Try the quick test bounds written question

Learning how to use upper and lower bounds can be relatively straightforward but:

- Don’t think about ’rounding’ numbers – even though the question talks about 3 significant figures. In a sense, the 3 sig fig. bit is only useful to calculate the lower bound – then the upper bound can be estimated. If you remember that learning how to use upper and lower bounds is really manufacturing tolerances, you should be OK.
- Don’t try to ‘short cut’ the question by just working out the bits you need. It’s better to draw a chart – like the video – and work out upper / lower bounds for each number. You might need them later in the question; and it’ll show the examiner that you’ve considered all the options.

## I said 24.45999999999999999mm!

View the video on YouTube:

How to use upper and lower bounds

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