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mathematicsprinted 13 · PDF 14
165 pagesrevision 46935
printed 13 · PDF 14
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The following table shows some more complex properties of powers and
roots:
Property
Example
(am)n = amn
(33)2 = (3*3*3)*(3*3*3) = 36 = 33*2
am/n = n√am
33/2 = 33 * 1/2 = (33)1/2 = √33
(a/b)n = an/bn
(1/3)2 = (1/3)*(1/3) = (1*1)/(3*3) =
12/32
(a/b)-n = bn/an
(5/6)-1 = 1/(5/6) = 6/5 = (6/5)1
Topic: Limits of Accuracy (1.10)
Major Terms and associated formulas:
Error:
Range of numerical where actual value lies.
Formula:
Error = Scale Value / 2
*Scale value: The value which is physically readable on scale.
Solved example:
Q: A rectangle has length 10 cm and width 6cm. Both measurement are
nearest to cm. Find the error.
Solution:
*Nearest to cm = 1cm = Scale value
½= 0.5 cm Error = 0.5 cm
Upper Bound:
It means how high a number could be before rounded
Formula:
Upper bound = Error + Actual value
Lower Bound:
It means how low a number could be before rounded
Formula:
Lower bound = Actual value - Error
Solved example:
Q: A rectangle has length 10 cm and width 6cm. Both measurement are