Choose a language: English | Malayalam

Number (Intermediate) - Boundaries (Upper and Lower Class)
 
Upper and Lower Boundaries | Application to Problems
 
Upper and Lower Boundaries

The degree of accuracy in a measurement is often given in a question. This means that we have a maximum value (upper boundary) and a minimum value (lower boundary).

Example:
A length is measured as 15cm to the nearest cm.
 
Minimum value = 14.5cm
 
This is because 14.4 would be 14cm to the nearest cm.
 
Maximum value = 15.49999…cm

We are allowed to write this as 15.5cm.

Rule: If a measurement is accurate to a given amount, then the boundaries are half of that amount, above and below the measurement.
 
For example, 2.8cm to the nearest mm, given amount = 0.1
 
Maximum = 2.8 + 0.1/2 = 2.8 + 0.05 = 2.85
Minimum = 2.8 - 0.1/2 = 2.8 – 0.05 = 2.75

 

Application to Problems

Example 1:
Calculate the maximum value for the area of a rectangle of length 12cm and width 10cm measured to the nearest cm.

Maximum length = 12 + 0.5 = 12.5cm
Maximum width = 10 + 0.5 = 10.5cm
Maximum area = 12.5 x 10.5 = 131.25cm2

Example 2:
Find the maximum value of 500 ÷ 100 (figures given to the nearest 100)

Max.value of 500 = 500 + 50 = 550
Min.value of 100 = 100 – 50 = 50
Max. value of 500 ÷ 100 is 550 ÷ 50 = 11

Note: For division,

maximum is max. ÷ min.

minimum is min. ÷ max.
For subtraction,
 

maximum = max. – min.

minimum = min. – max.