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 3rd decimal 7 is greater than 5 , hence the 2nd decimal will be increased by 1 .

• 3.68459 will become 3.68 when rounded off to 2 decimal places. Here the 3rd decimal 4 is less than 5 , hence the 2nd 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 2nd digit is less than 5 , hence 62 becomes 60 nearest 10.
• 67 to the nearest 10 becomes 70 . Here the 2nd digit is greater than 7 , hence 67 becomes 70 nearest 10