# Upper and Lower Bounds

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

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This is level 5: mixed calculations involving upper and lower bounds. You can earn a trophy if you get at least 9 questions correct.

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This is Upper and Lower Bounds level 5. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 6

*** This question involves discreet data. The other questions you have answered involved continuous data. It makes a difference to your answer - you may need to ask your teacher for help.

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## Description of Levels

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Level 1 - Numbers truncated or rounded up or down to a given multiple.

Level 2 - Quantities rounded to the nearest multiple.

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

Level 4 - Discrete and continuous quantities rounded to a number of significant figures.

Level 5 - Mixed calculations involving upper and lower bounds.

Level 6 - Upper and lower bounds of algebraic expressions.

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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.

## Help Video

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