Question Type 4: Using rounded numbers in calculations and accounting for them in final solutions Exercises

Given $p = 1.234$ (rounded to the nearest thousandth), find the lower and upper bounds of $p^3$. Give your answers to 4 decimal places.

Given $r = 7.8$ (rounded to the nearest tenth), find the maximum and minimum possible values of $r^2$.

Given $x = 5.2$ (rounded to the nearest tenth) and $y = 3.8$ (rounded to the nearest tenth), find the maximum and minimum possible values of the product $xy$.

Given $x = 4.5$ (rounded to the nearest tenth) and $y = 5.34$ (rounded to the nearest hundredth), find the maximum and minimum possible values of $xy^2$.

Given $s = 0.125$ (rounded to the nearest thousandth), find the maximum and minimum possible values of $\sqrt{s}$.

Given speed $v = 60.4\,$km/h (rounded to the nearest tenth) and time $t = 2.0\,$h (rounded to the nearest tenth), find the maximum and minimum possible values of the distance $d = vt$.

Given length $L = 2.45\,\text{m}$ (rounded to the nearest centimetre) and width $W = 1.3\,\text{m}$ (rounded to the nearest tenth), find the maximum and minimum possible values of the area $A = L \times W$. Give your answers rounded to four decimal places.

Given $m = 12.5$ (rounded to the nearest tenth) and $n = 5.25$ (rounded to the nearest hundredth), find the maximum and minimum possible values of $2m - 3n$.

Given $a = 2.15$ (rounded to the nearest hundredth) and $b = 1.3$ (rounded to the nearest tenth), find the maximum and minimum possible values of the quotient $\frac{a}{b}$.

The volume of a liquid is measured as $V = 3.50\,\text{L}$, rounded to the nearest hundredth of a litre. The mass is measured as $m = 7.2\,\text{kg}$, rounded to the nearest tenth of a kilogram.

Calculate the maximum and minimum possible values for the density $\rho = \frac{m}{V}$, and hence state the range of possible values for $\rho$. Give your answers to 3 decimal places.

Given $x = 0.99$ (rounded to the nearest hundredth), find the maximum and minimum possible values of $\frac{1}{1 - x}$.