This worksheet is about **lower and upper bounds**.

Suppose we've rounded a number to the nearest whole number and get 14.

Numbers that round up to 14 include 13.9, 13.75, 13.694, 13.5. The smallest of these is 13.5. This is called the **LOWER BOUND**.

Anything smaller will round down to 13.

Larger numbers that round down to 14 include 14.1, 14.34968, 14.49. The largest of these is 14.4999999... This is the **UPPER BOUND**, which we write as 14.5.

We write these bounds as an inequality.

13.5 ≤ n < 14.5

__ Note:__ The lower bound is

__included__in the inequality, but the upper bound is not – it would round up.

**Example**

Find the upper and lower bounds for 8500 which has been rounded to the nearest hundred.

8499, 8470, 8450 would round up.

8450 is the smallest, so this is the **LOWER BOUND**.

8501, 8548, 8549 would round down.

8549.999999 is the largest, so we say that 8550 is the** UPPER BOUND**.

8450 ≤ n < 8550