Найдите частное:
\(\displaystyle 3:16=\),
Поделим \(\displaystyle 3\) на \(\displaystyle 16\) в столбик:
| \(\displaystyle 3\) | \(\displaystyle 1\) | \(\displaystyle 6\) |
| \(\displaystyle ?\) |
Первое действие.
Так как \(\displaystyle 3<16\) и больше разрядов у числа нет, то пишем нуль первой цифрой в частном и ставим запятую после него:
| \(\displaystyle 3\) | \(\displaystyle 1\) | \(\displaystyle 6\) | |
| \(\displaystyle \color{blue}{0}\) | \(\displaystyle \color{red}{,}\) | \(\displaystyle ?\) |
и добавляем нуль к делимому справа (то есть к \(\displaystyle 3\) справа):
| \(\displaystyle 3\) | \(\displaystyle \color{red}{0}\) | \(\displaystyle 1\) | \(\displaystyle 6\) | |
| \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle ?\) |
Второе действие.
Делим \(\displaystyle 30\) на \(\displaystyle 16\):
\(\displaystyle 30= \color{green}{1}·16+14=\color{blue}{16}+14\).
пишем \(\displaystyle \color{green}{1}\) в частном и вычитаем \(\displaystyle 30-\color{blue}{16}=\bf14\):
| \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 1\) | \(\displaystyle 6\) | |||
| \(\displaystyle -\) | \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle \color{green}{1}\) | \(\displaystyle ?\) | ||
| \(\displaystyle \color{blue}{1}\) | \(\displaystyle \color{blue}{6}\) | |||||
| \(\displaystyle \bf1\) | \(\displaystyle \bf4\) |
Третье действие.
Добавляем нуль к разности справа:
| \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 1\) | \(\displaystyle 6\) | ||||
| \(\displaystyle -\) | \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle 1\) | \(\displaystyle ?\) | |||
| \(\displaystyle 1\) | \(\displaystyle 6\) | ||||||
| \(\displaystyle 1\) | \(\displaystyle 4\) | \(\displaystyle \color{red}{0}\) |
Делим \(\displaystyle 140\) на \(\displaystyle 32\):
\(\displaystyle 140= \color{green}{8}·16+12=\color{blue}{128}+12\).
Пишем \(\displaystyle \color{green}{8}\) в частном и вычитаем \(\displaystyle 140-\color{blue}{128}=\bf12\):
| \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 1\) | \(\displaystyle 6\) | |||||
| \(\displaystyle -\) | \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle 1\) | \(\displaystyle \color{green}{8}\) | \(\displaystyle ?\) | |||
| \(\displaystyle 1\) | \(\displaystyle 6\) | |||||||
| \(\displaystyle 1\) | \(\displaystyle 4\) | \(\displaystyle 0\) | ||||||
| \(\displaystyle -\) | ||||||||
| \(\displaystyle \color{blue}{1}\) | \(\displaystyle \color{blue}{2}\) | \(\displaystyle \color{blue}{8}\) | ||||||
| \(\displaystyle \bf1\) | \(\displaystyle \bf2\) |
Четвертое действие.
Добавляем нуль к разности справа:
| \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 1\) | \(\displaystyle 6\) | ||||||
| \(\displaystyle -\) | \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle 1\) | \(\displaystyle 8\) | \(\displaystyle ?\) | ||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | ||||||||
| \(\displaystyle 1\) | \(\displaystyle 4\) | \(\displaystyle 0\) | |||||||
| \(\displaystyle -\) | |||||||||
| \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle 8\) | |||||||
| \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle \color{red}{0}\) |
Делим \(\displaystyle 120\) на \(\displaystyle 16\):
\(\displaystyle 120= \color{green}{7}·16+16=\color{blue}{112}+8\).
Пишем \(\displaystyle \color{green}{7}\) в частном и вычитаем \(\displaystyle 120-\color{blue}{112}=\bf8\):
| \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 1\) | \(\displaystyle 6\) | |||||||
| \(\displaystyle -\) | \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle 1\) | \(\displaystyle 8\) | \(\displaystyle \color{green}{7}\) | \(\displaystyle ?\) | ||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | |||||||||
| \(\displaystyle 1\) | \(\displaystyle 4\) | \(\displaystyle 0\) | ||||||||
| \(\displaystyle -\) | ||||||||||
| \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle 8\) | ||||||||
| \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle 0\) | ||||||||
| \(\displaystyle -\) | ||||||||||
| \(\displaystyle \color{blue}{1}\) | \(\displaystyle \color{blue}{1}\) | \(\displaystyle \color{blue}{2}\) | ||||||||
| \(\displaystyle \bf8\) |
Пятое действие.
Добавляем нуль к разности справа:
| \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 1\) | \(\displaystyle 6\) | ||||||||
| \(\displaystyle -\) | \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle 1\) | \(\displaystyle 8\) | \(\displaystyle 7\) | \(\displaystyle ?\) | |||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | ||||||||||
| \(\displaystyle 1\) | \(\displaystyle 4\) | \(\displaystyle 0\) | |||||||||
| \(\displaystyle -\) | |||||||||||
| \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle 8\) | |||||||||
| \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle 0\) | |||||||||
| \(\displaystyle -\) | |||||||||||
| \(\displaystyle 1\) | \(\displaystyle 1\) | \(\displaystyle 2\) | |||||||||
| \(\displaystyle 8\) | \(\displaystyle \color{red}{0}\) |
Делим \(\displaystyle 80\) на \(\displaystyle 16\):
\(\displaystyle 80= \color{green}{5}·16=\color{blue}{80}\).
Пишем \(\displaystyle \color{green}{5}\) в частном и вычитаем \(\displaystyle 80-\color{blue}{80}=\bf0\):
| \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 1\) | \(\displaystyle 6\) | ||||||||
| \(\displaystyle -\) | \(\displaystyle 0\) | \(\displaystyle ,\) | \(\displaystyle 1\) | \(\displaystyle 8\) | \(\displaystyle 7\) | \(\displaystyle \color{green}{5}\) | |||||
| \(\displaystyle 1\) | \(\displaystyle 6\) | ||||||||||
| \(\displaystyle 1\) | \(\displaystyle 4\) | \(\displaystyle 0\) | |||||||||
| \(\displaystyle -\) | |||||||||||
| \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle 8\) | |||||||||
| \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle 0\) | |||||||||
| \(\displaystyle -\) | |||||||||||
| \(\displaystyle 1\) | \(\displaystyle 1\) | \(\displaystyle 2\) | |||||||||
| \(\displaystyle 8\) | \(\displaystyle 0\) | ||||||||||
| \(\displaystyle -\) | |||||||||||
| \(\displaystyle \color{blue}{8}\) | \(\displaystyle \color{blue}{0}\) | ||||||||||
| \(\displaystyle \bf0\) |
Таким образом, \(\displaystyle 3:16=0,1875\).
Ответ: \(\displaystyle 0,1875\).