IB Mathematics Applications & Interpretation 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 $x{y}^2$.

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 $\frac{1}{1-x}$.