Calculating With Bounds: Addition and Subtraction

Two lengths are given as $5.2$ cm and $3.7$ cm, both to $1$ decimal place. Find the maximum and minimum possible total length.

• 1Bounds of $5.2$: $5.15$ to $5.25$. Bounds of $3.7$: $3.65$ to $3.75$
• 2Maximum total = max + max = $5.25+3.75=9.00$
• 3Minimum total = min + min = $5.15+3.65=8.80$

Answer: Maximum = $9.00$ cm, Minimum = $8.80$ cm

Two masses are given as $12$ kg and $4$ kg, both rounded to the nearest whole kg. Find the maximum and minimum possible value of ($12$ kg − $4$ kg).

• 1Bounds of $12$: $11.5$ to $12.5$. Bounds of $4$: $3.5$ to $4.5$
• 2Maximum difference = max($12$) − min($4$) = $12.5-3.5=9.0$
• 3Minimum difference = min($12$) − max($4$) = $11.5-4.5=7.0$

Answer: Maximum = $9.0$ kg, Minimum = $7.0$ kg