# Upper and Lower Bounds

## Determine the upper and lower bounds when rounding or truncating quantities used in calculations.

##### Level 1Level 2Level 3Level 4Level 5Exam-StyleDescriptionHelpMore Rounding

This is level 2: quantities rounded to a given multiple. You can earn a trophy if you get at least 7 questions correct.

 1. The length of a pencil, p millimetres, is rounded to the nearest ten millimetres. The length is given as 200mm. What are the limits of accuracy? ≤ p < 2. A set of kitchen scales displays readings to the nearest ten grams. Find the upper and lower bounds in grams for a weight, w, displayed as 250g.250g ≤ w < 3. A digital thermometer measures temperatures (T) to the nearest two degrees. Find the range of possible temperatures if the display shows 72o.72o ≤ T < 4. A number, D, is rounded to the nearest ten. The result is 480. What are the limits of accuracy? ≤ D < 5. The numbers of pins in a box (n) is rounded to the nearest fifty. If the number of pins is given as 2950 find the smallest and largest number of pins that could be in the box. ≤ n < 6. A number, F, is rounded to the nearest fifty. The result is 3250. What are the limits of accuracy? ≤ F < 7. The numbers of supporters at a football match (S) is rounded to the nearest fifty. If the number of supporters is given as 3750 find the range of values within which the actual number of supporters could be. ≤ S < 8. A number, H, is rounded to the nearest twenty. The result is 1740. What are the limits of accuracy? ≤ H < 9. A plumbing supplier sells pipes cut to size. The length (L millimetres) of the cut pipe is rounded to the nearest twenty millimetres in order to calculate the cost. If the length of a particular piece of pipe is given as 1980 find the range of values within which the actual length could be. ≤ L < 10. A number, J, is rounded to the nearest one hundred. The result is 10700. What are the limits of accuracy? ≤ J <
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This is Upper and Lower Bounds level 2. You can also try:
Level 1 Level 3 Level 4 Level 5

## Instructions

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## Description of Levels

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Level 1 - Numbers truncated to a given multiple.

Level 2 - Quantities rounded to a given multiple.

Level 3 - Numbers rounded to a number of decimal places.

Level 4 - Quantities rounded to a number of significant figures.

Level 5 - Calculations involving upper and lower bounds.

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## Extension

Students who are also studying Physics may want to investigate a topic called Propagation of Uncertainties that uses these formulas.

$$\text{If} \quad y= a \pm b \quad \text{then} \quad \Delta y = \Delta a + \Delta b$$ $$\text{If} \quad y= \frac{ab}{c} \quad \text{then} \quad \frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c}$$ $$\text{If} \quad y= a^n \quad \text{then} \quad \frac{\Delta y}{y} = \begin{vmatrix} n \frac{\Delta a}{a} \end{vmatrix}$$

The triangular symbols are the Greek letter delta and represent the errors or, more accurately, uncertainties.

## Examples

This video is from the excellent Corbettmaths.

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