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Консультация № 190802
28.03.2017, 21:32
0.00 руб.
0
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Найти предельные абсолютные и относительные погрешности чисел если они имеют только верные цифры: а)в узком б) в широком смысле.
а)41.72. б)0,678.
Найти предельные абсолютные и относительные погрешности чисел если они имеют только верные цифры: а)в узком б) в широком смысле.
а)41.72. б)0,678.
Обсуждение
29.03.2017, 08:56
общий
это ответ
Здравствуйте, freekly!
а) Если приближённое число
имеет только верные цифры в узком смысле, то его абсолютная погрешность 
не превышает половины единицы десятичного разряда, выражаемого последней цифрой 
То есть выполняется неравенство
Для предельной абсолютной погрешности
приближённого числа 
выполняется неравенство
Поэтому можно принять, что предельная абсолютная погрешность приближённого числа составляет
Тогда предельная относительная погрешность приближённого числа составляет
или 
б) Если приближённое число
имеет только верные цифры в широком смысле, то его абсолютная погрешность не превышает единицы десятичного разряда, выражаемого последней цифрой 
То есть выполняется неравенство
Для предельной абсолютной погрешности приближённого числа выполняется неравенство
Поэтому можно принять, что предельная абсолютная погрешность приближённого числа составляет
Тогда предельная относительная погрешность приближённого числа составляет
или 
а) Если приближённое число
имеет только верные цифры в узком смысле, то его абсолютная погрешность не превышает половины единицы десятичного разряда, выражаемого последней цифрой То есть выполняется неравенствоДля предельной абсолютной погрешности
приближённого числа выполняется неравенствоПоэтому можно принять, что предельная абсолютная погрешность приближённого числа
составляетТогда предельная относительная погрешность приближённого числа
составляет или б) Если приближённое число
имеет только верные цифры в широком смысле, то его абсолютная погрешность не превышает единицы десятичного разряда, выражаемого последней цифрой То есть выполняется неравенствоДля предельной абсолютной погрешности
приближённого числа выполняется неравенствоПоэтому можно принять, что предельная абсолютная погрешность приближённого числа
составляетТогда предельная относительная погрешность приближённого числа
составляет или
Об авторе:
Facta loquuntur.
Facta loquuntur.
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