Upper and Lower BoundsDetermine the upper and lower bounds when rounding quantities used in calculations. 
This is level 2: quantities rounded to the nearest multiple. You can earn a trophy if you get at least 7 questions correct.
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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.
Exam Style questions are in the style of GCSE or IB/Alevel exam paper questions and worked solutions are available for Transum subscribers.
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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.
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