IB Mathematics Applications & Interpretation Question Type 3: Determining Maximum and Minimum Values for a Rounded Number Exercises

The area of a field is recorded as $15.24{\text{ m}}^2$, rounded to the nearest hundredth. Determine the maximum and minimum possible areas.

A water tank volume $V$ is rounded to two decimal places giving $V=2.50$ litres. Find the range of possible volumes.

A voltage measurement $V=12.6$V is rounded to the nearest $0.1$V. Find the maximum percentage error in this reading.

Two rods have lengths $x=5.12\text{m}$ and $y=3.48\text{m}$, both rounded to the nearest $0.01\text{m}$. Find the maximum and minimum possible values of their total length $T=x+y$.

Given that $x=5.69$ is rounded to the nearest $0.01$, find the minimum and maximum possible values of $x$.

A mass, $m$, is measured as $0.056$ kg, rounded to the nearest thousandth. Find the minimum possible value, $m_{\min }$, and the maximum possible value, $m_{\max }$.

A container has volume $1.25\text{L}$, rounded to two decimal places. If this volume is poured equally into 5 identical bottles, what are the possible minimum and maximum volumes in each bottle?

A measurement $y$ is recorded as $12.345$ rounded to the nearest $0.001$. Determine the lower and upper bounds for the actual value of $y$.

Given a number $z$ rounded to the nearest whole number is $78$, determine the upper and lower bounds for $z$.

A length $a=7.3$cm is rounded to the nearest tenth. Find the possible range of $a$.

The total cost of groceries is recorded as $31.40, rounded to the nearest $0.10. Find the bounds for the actual cost.