Degree of accuracy

Definition

The degree of accuracy is a measurement of how close a given measurement is to the true value. It helps us identify the quality of measurements by checking that they are accurate

Depending on the context, it may not always be necessary to give an exact answer to a measurement. At other times, it is actually more acceptable to have rounded the amount to an appropriate degree of accuracy. The population of countries is often quoted in millions because the exact figure changes constantly. For example, the population of the UK is ‘about 65 million’.

It can also depend on what you are going to do with the measurement. For example, when measuring a window for curtains, the width to the nearest $5$ cm would be more than sufficient. But if you are measuring the same window for a replacement pane of glass, a much higher degree of accuracy would be needed.

It should be understood that measurement is continuous, so lengths, weights, etc. can take any value on the number line including decimals and fractions. This is in contrast to amounts which are counted, such as the number of sweets in a jar, which can only take whole number values. However, large numbers of items to be counted may act as continuous measures, such as national population sizes.

Accuracy is often quoted using the number of decimal places. If you need to round a measurement to $1$ decimal place that implies to the nearest one-tenth. If you need to round a measurement to $2$ decimal places that implies to the nearest one-hundredth.

Examples

• $3.68759$ will become $3.69$ when rounded off to $2$ decimal places. Here the $3$^rd decimal $7$ is greater than $5$ , hence the $2$^nd decimal will be increased by $1$.

• $3.68459$ will become $3.68$ when rounded off to $2$ decimal places. Here the $3$^rd decimal $4$ is less than $5$ , hence the $2$^nd decimal will remain same.
• $465$ to the nearest $100$ becomes $500$ . Here $65$ is greater than $50$, hence $465$ becomes $500$ nearest $100$.
• $435$ to the nearest $100$ becomes $400$ . Here $35$ is less than $50$, hence $435$ becomes $400$ nearest $100$.
• $62$ to the nearest $10$ becomes $60$ . Here the $2$^nd digit $2$ is less than $5$ , hence $62$ becomes $60$ nearest $10$.
• $67$ to the nearest $10$ becomes $70$ . Here the $2$^nd digit $7$ is greater than $5$ , hence $67$ becomes $70$ nearest $10$,