# How to calculate the lower bound and upper bound. Math number help.

## Lower And Upper Bound Video

When a number is rounded off, the lower bound is the smallest possible value that the number could have been, and the upper bound is the highest possible value that the number could have been.

Let’s take a look at a few questions on finding the lower and upper bounds.

**Example 1**

At an airport, a suitcase is weighed as 30kg rounded to the nearest 10kg. Work out the lower and upper bounds of the suitcase.

Since the number is rounded to the nearest 10 the scale that the bag is weighed on is increasing by 10. So the lower bound is halfway between 20 and 30 which is 25kg. Also, the upper bound is halfway between 30 and 40. So the upper bound is 35kg.

**Example 2**

The length of a piece of paper is measured as 27.6cm rounded to 1 decimal place. Calculate the lower and upper bound of the length of the piece of paper.

Since the number is rounded to 1 decimal place the scale is increasing by 0.1. So the lower bound is halfway between 27.5 and 27.6 which is 27.55cm. Also, the upper bound is halfway between 27.6 and 27.7. So the upper bound is 27.65kg.

**Example 3**

A sprinter finishes a race in 8.83 seconds. Work out the sprinters slowest and fastest possible times if the time is accurate to 3 significant figures.

Since the number is rounded to 3 significant figures the scale is increasing in 0.01. So the lower bound is halfway between 8.82 and 8.83 which is 8.825 seconds. Also, the upper bound is halfway between 8.83 and 8.84 which is 8.835 seconds.

So the slowest possible time is 8.835 seconds and the fastest possible time is 8.825 seconds.

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