In a DIY store, the height of a door is given as 195 cm to the nearest cm. Write down the upper bound for the height of the door.
The correct answer and explanation is:
The height of the door is given as 195 cm to the nearest cm. This means the measurement has been rounded to the nearest whole number. To find the upper bound for the height of the door, it is important to understand how rounding works.
When a measurement is rounded to the nearest cm, it could have been any value between 194.5 cm and 195.5 cm. The number 195 cm represents the value that was rounded from a range of values. Therefore, the upper bound for the height of the door is the value that is just below the next possible rounded value, which is 195.5 cm.
In general, the rule for rounding to the nearest whole number is that if a decimal value is 0.5 or greater, the number is rounded up. If the decimal value is less than 0.5, the number is rounded down. Hence, the range of values that would round to 195 cm is from 194.5 cm (the lower bound) to 195.5 cm (the upper bound). Since the upper bound is the largest possible value that would still be rounded to 195 cm, the upper bound is 195.5 cm.
Thus, the correct answer is that the upper bound for the height of the door is 195.5 cm. This means that the height of the door is any value that is less than or equal to 195.5 cm but greater than or equal to 194.5 cm.