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Upper and Lower Bounds

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

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This is level 2: quantities rounded to the nearest 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 190mm. What are the limits of accuracy?

Pencil
p < Correct Wrong
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 290g.

Scales

290g

g ≤ w < g Correct Wrong
3. A digital thermometer measures temperatures (T) to the nearest two degrees. Find the range of possible temperatures if the display shows 66o.

66o

oT < o Correct Wrong
4. A number, D, is rounded to the nearest ten. The result is 460. What are the limits of accuracy? ≤ D < Correct Wrong
5. The weight of a box of bolts (w) is rounded to the nearest 50g. If the weight of the box is given as 2850g What are the limits of accuracy. g ≤ w < g Correct Wrong
6. A number, F, is rounded to the nearest fifty. The result is 3050. What are the limits of accuracy? ≤ F < Correct Wrong
7. The length of a fibre-optic cable (L) is rounded to the nearest fifty metres. If the length is given as 3700m find the range of values within which the actual length of the cable could be. m ≤ L < m Correct Wrong
8. A number, H, is rounded to the nearest twenty. The result is 1800. What are the limits of accuracy? ≤ H < Correct Wrong
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 1800 find the range of values within which the actual length could be. L < Correct Wrong
10. A number, J, is rounded to the nearest one hundred. The result is 10200. What are the limits of accuracy? ≤ J < Correct Wrong
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This is Upper and Lower Bounds level 2. You can also try:
Level 1 Level 3 Level 4 Level 5 Level 6

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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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.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

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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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