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 15 cm to the nearest cm.
Minimum value = 14,5 cm
This is because 14,4 would be 14 cm to the nearest cm.
Maximum value = 15,49999…cm
We are allowed to write this as 15,5 cm.
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, 2,8 cm to the nearest mm; given amount = 0,1.
Maximum = 2,8 +  = 2,8 + 0,05 = 2,85
Minimum = 2,8 - = 2,8 – 0,05 = 2,75 |
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Application to Problems
Example 1: Calculate the maximum value for the area of a rectangle of length 12 cm and width 10 cm measured to the nearest cm.
Maximum length = 12 + 0,5 = 12,5 cm
Maximum width = 10 + 0,5 = 10,5 cm
Maximum area = 12,5 x 10,5 = 131,25 cm2
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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.
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For subtraction,
maximum = max. – min.
minimum = min. – max.
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