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Консультация № 191340
12.09.2017, 19:13
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Помогите, пожалуйста, решить данные задания, а то совсем не получается. Либо есть какие-нибудь примеры похожих заданий
Помогите, пожалуйста, решить данные задания, а то совсем не получается. Либо есть какие-нибудь примеры похожих заданий
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Обсуждение
12.09.2017, 21:59
общий
это ответ
Здравствуйте, dimabylk!
Рассмотрим задание 3: "Определить количество верных значащих цифр в числе x* и округлить его до верных цифр, если известна относительная погрешность x*:
Для решения задачи определения количества n верных знаков числа a, если известна относительная погрешность [$948$], обычно используют приближённую формулу для абсолютной погрешности [$916$][$8776$]a[$948$]. Учитывая старший десятичный разряд [$945$] числа a, можно определить количество верных знаков данного приближённого числа a. В частности, если [$948$][$8804$]1/10[sup]n[/sup], то [$948$][$8804$]([$945$]+1)[$183$]10[sup]m[/sup][$183$]10[sup]-n[/sup][$8804$]10[sup]m-n+1[/sup], где число a имеет заведомо n верных десятичных знаков (в широком смысле).
Согласно условию задачи, a=197,3587,~[$948$]=0,07, m=2. Тогда
откуда n=1. Поэтому нужно заданное число нужно записать так: 2[$183$]10[sup]2[/sup], или, добавляя одну сомнительную цифру, так: 2,0[$183$]10[sup]2[/sup].
Рассмотрим задание 3: "Определить количество верных значащих цифр в числе x* и округлить его до верных цифр, если известна относительная погрешность x*:
x*=197,3587; [$916$]x*=7 %".
Для решения задачи определения количества n верных знаков числа a, если известна относительная погрешность [$948$], обычно используют приближённую формулу для абсолютной погрешности [$916$][$8776$]a[$948$]. Учитывая старший десятичный разряд [$945$] числа a, можно определить количество верных знаков данного приближённого числа a. В частности, если [$948$][$8804$]1/10[sup]n[/sup], то [$948$][$8804$]([$945$]+1)[$183$]10[sup]m[/sup][$183$]10[sup]-n[/sup][$8804$]10[sup]m-n+1[/sup], где число a имеет заведомо n верных десятичных знаков (в широком смысле).
Согласно условию задачи, a=197,3587,~[$948$]=0,07, m=2. Тогда
[$948$][$8776$]197,3587[$183$]0,07[$8776$]13,7,
13,7[$8804$]10[sup]2-n+1[/sup],
13,7[$8804$]10[sup]3-n[/sup],
откуда n=1. Поэтому нужно заданное число нужно записать так: 2[$183$]10[sup]2[/sup], или, добавляя одну сомнительную цифру, так: 2,0[$183$]10[sup]2[/sup].
Об авторе:
Facta loquuntur.
Facta loquuntur.
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