# 1.4. Estimate quantities to a tolerance justified in the need

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As you saw in the example of the swimming pool, it is important to choose the correct unit of measurement, as it is clumsy to say a pool is 25 000 mm long. Sometimes it is also inconvenient to have to accurately measure something, when a quick estimate will do. We can at times just estimate quantities to a tolerance justified in the context of the need, as we will discuss below.

Estimation is about making conjectures / guessing what the outcome of the measurement would be. It is always import that you justify your estimation after the actual measurement has been done.

Estimation allows us to arrive at a ‘nearly correct’ answer that is close enough for all practical purposes; for example, when we want to estimate the size of a room, we will not necessarily measure it with a measuring tape, but give large steps that are roughly equal to a metre.

If you measure a space such as a room, then you will estimate the length and breadth by using a stride. A stride is a very large step and is the distance between the heel of the back foot and the toe of the front foot. In this case we are ‘estimating’ the size of the room.

If you measure the length of your classroom for the purpose of finding out if it is shorter or longer than the class next door, and you find the length to be 8m while it is actually 825cm, then your measurement is not far out, because a difference of 250mm for the purpose for which you required the length is of no importance.

If, however, a carpenter measures the width of a door that has to fit into a doorpost and makes it 790mm, when it should be 810 mm, he is making a big mistake, because for this purpose a difference of 20mm is very important.

Any measurement made with a measuring device is approximate. If you measure the same object on two different occasions, the two measurements may not be the same. The difference between two measurements is called a **variation **in the measurements**. **

Another word for this variation – or uncertainty in measurement – is** “error”.** This “error” is not the same as a “mistake”. It does not mean that you got the wrong answer. The error in measurement is a mathematical way to show the uncertainty in the measurement.

The **smallest unit to which it can measure determines the precision of a measuring instrument**. The precision is said to be the same as the smallest fractional or decimal division on the scale of the measuring instrument.

**Accuracy** is the measure of how close the result of the measurement comes to the “true” value.

There are specific situations at home or at work where one has to be absolutely accurate (correct) in measurement otherwise it could end up being costly. By familiarising ourselves with different types of measuring units, we will become better equipped at home and in the workplace.

**Tips for estimation, measurement and calculations **

If you need to measure a large rectangular space, such as a room to be carpeted, you must make sure that you measure the length and width of the room carefully. If the measurements are not accurate then you could end up buying too much or too little carpet!

Always:

- estimate the outcome (area of the space)
- measure accurately
- check, have you used the same units of measurement
- then calculate (work out the area)