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te E, < i ax 107" ' ia a 3 x 10 "TX TQ 2k x 10"-2—] < Ps kx 10"-2 se ] Hence the theorem is true in al] Cases Verification of the theorem - 342 67392—0°000005 342673920—5 I . 1 2x 34267292—1 2(34267392 — 3) Seema a The following rales may be kept in mind while working with approximate numbers, Rule 1, The absolute error of an algebraic sum of several approximate numbers is equal to the sum of the absolute errors of the individual numbers. Ex, 1.1. Consider the sum of the approximate numbers 0°346, 0°1854, 345°2, 235°4, 11°53, 9°49, 0°0836, 0°0227, 0:00123, 0 000321 all their digits being correct upto the figures shown. Find the absolute error of the sum. Solution: Maximum absolute error of the given set of numbers is 005 being present in 345°2 and 2354. Hence the maximum absolute error in the sum amounts to 2x0°05=0'1. To find the’sum weround-off the numbers uptotwo decimal places and add. Thus S=345'2+ 235°44 11°534+9°49+0°35+0°19+008+0°02 = 602°26. Rounding it again upto the correct figure gives, S=~602°3. Total rounding error is 004+0'1. 
