🎯 Nailing Bounds: Mastering Upper & Lower Limits of Accuracy!

When exam questions give measurements that have been rounded, your task is to find the **true range** in which the exact value lies. Understanding limits of accuracy not only secures easy marks but also prevents over- or under-estimating results in real-life tasks like construction and science experiments.

What are Upper & Lower Bounds?

If a value is rounded to the _nearest_ unit (1, 0.1, 0.01, etc.), its **upper bound** is halfway _above_ and its **lower bound** is halfway _below_ the stated number. For example,

12.3

cm (nearest

0.1

cm) means

12.25 \le x < 12.35

. **Remember:** the lower bound is inclusive, the upper bound is exclusive!

Worked Example: Perimeter of a Rounded Rectangle

Problem: The length of a rectangle is

12.3

cm and the width is

7.8

cm, each measured to the nearest

0.1

cm. Find the upper and lower bounds of the rectangle’s area. Solution Steps:
1. Identify bounds for each side:

12.25 \le L < 12.35

and

7.75 \le W < 7.85

.
2. Lower bound for area:

A_{\text{min}} = 12.25 \times 7.75 = 94.9375\text{ cm}^2

3. Upper bound for area:

A_{\text{max}} = 12.35 \times 7.85 = 96.9975\text{ cm}^2

4. Therefore the true area satisfies

94.94\text{ cm}^2 \le A < 97.00\text{ cm}^2.

Practice creating bounds every time you meet rounded data. **Drill this skill and you’ll never lose accuracy marks!**