There are two types of measures.

**Discrete** measures can be counted (such as people, or cars).

**Continuous** measures involve measurement (such as the length of a car, or the weight of a person) where a single measure can fall into a range.

The **accuracy** of a continuous measurement depends upon the person or device making the measurement. Sometimes this is stated as *25m to the nearest 1m*. This can be written as 24.5 ≤ *l* < 25.5. Half of the *nearest 1m* goes above the given value, and half goes below.

In engineering, a measurement is often given with an **error interval** or **tolerance**: for example, a length may be given as 25cm ±0.5mm: this describes the accuracy of the measurement in a slightly different way.

However it is stated, the range is the **Limit of Accuracy** for that measurement.

The Limit of Accuracy gives us two additional values. If *m* is the measurement and *t* is the tolerance, then:

**lower bound** = *m* - 0.5*t*; and

**upper bound** = *m* + 0.5*t*.

A car is 432cm long, measured with an error interval of 0.15cm. What are the upper and lower bounds of the length of the car? Write the answer as an inequality.

Lower: 432 - 0.15 = 431.85

Upper: 432 + 0.15 = 432.15

Answer: 431.85 ≤ length < 432.15 cm

A lorry makes a run from Manchester to Leeds and return three times over one week. The distance from Manchester to Leeds is 44.8 miles to the nearest 0.1 miles.

What is the minimum distance the lorry could have travelled?

Minimum for one one-way journey: 44.8 - 0.05 = 44.75.

For six (three return) journeys = 44.75 x 6 = 268.5.

Answer: 268.5 miles

See also Inequalities in Rounding and Inequalities on a Number Line

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