Представьте \(\displaystyle -\frac{703}{625}\) в виде десятичной дроби.
Способ \(\displaystyle 1{\small.}\)
Представим в виде десятичной дроби число \(\displaystyle \frac{703}{625}{\small.}\) Для этого разделим числитель дроби на её знаменатель. Получим
| \(\displaystyle -\) | \(\displaystyle 7\) | \(\displaystyle 0\) | \(\displaystyle 3\) | \(\displaystyle 6\) | \(\displaystyle 2\) | \(\displaystyle 5\) | ||||||
| \(\displaystyle 6\) | \(\displaystyle 2\) | \(\displaystyle 5\) | \(\displaystyle 1\) | \(\displaystyle ,\) | \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle 4\) | \(\displaystyle 8\) | ||||
| \(\displaystyle -\) | \(\displaystyle 7\) | \(\displaystyle 8\) | \(\displaystyle 0\) | |||||||||
| \(\displaystyle 6\) | \(\displaystyle 2\) | \(\displaystyle 5\) | ||||||||||
| \(\displaystyle -\) | \(\displaystyle 1\) | \(\displaystyle 5\) | \(\displaystyle 5\) | \(\displaystyle 0\) | ||||||||
| \(\displaystyle 1\) | \(\displaystyle 2\) | \(\displaystyle 5\) | \(\displaystyle 0\) | |||||||||
| \(\displaystyle -\) | \(\displaystyle 3\) | \(\displaystyle 0\) | \(\displaystyle 0\) | \(\displaystyle 0\) | ||||||||
| \(\displaystyle 2\) | \(\displaystyle 5\) | \(\displaystyle 0\) | \(\displaystyle 0\) | |||||||||
| \(\displaystyle -\) | \(\displaystyle 5\) | \(\displaystyle 0\) | \(\displaystyle 0\) | \(\displaystyle 0\) | ||||||||
| \(\displaystyle 5\) | \(\displaystyle 0\) | \(\displaystyle 0\) | \(\displaystyle 0\) | |||||||||
| \(\displaystyle 0\) |
Таким образом,
\(\displaystyle \frac{703}{625}=1{,}1248{\small.}\)
Тогда
\(\displaystyle -\frac{703}{625}=-1{,}1248{\small.}\)
Способ \(\displaystyle 2{\small.}\)
Число \(\displaystyle \frac{703}{625}\) в виде дроби со знаменателем \(\displaystyle 10\) представить не получится: \(\displaystyle 10\) не делится на \(\displaystyle 625\small.\)
Число \(\displaystyle \frac{703}{625}\) в виде дроби со знаменателем \(\displaystyle 100\) представить не получится: \(\displaystyle 100\) не делится на \(\displaystyle 625\small.\)
Число \(\displaystyle \frac{703}{625}\) в виде дроби со знаменателем \(\displaystyle 1000\) представить не получится: \(\displaystyle 1000\) не делится на \(\displaystyle 625\small.\)
Для представления \(\displaystyle \frac{703}{625}\) в виде дроби со знаменателем \(\displaystyle 10000\) заметим, что \(\displaystyle 10000:625=16\small.\)
По основному свойству дроби, домножая и числитель, и знаменатель на \(\displaystyle \color{blue}{16}\small,\) получим
\(\displaystyle \frac{703}{625}=\frac{703\cdot \color{blue}{16}}{625\cdot \color{blue}{16}}=\frac{11248}{10000}=1{,}1248\small.\)
Тогда
\(\displaystyle -\frac{703}{625}=-1{,}1248{\small.}\)
Ответ: \(\displaystyle -1{,}1248{\small.}\)