分数转小数计算器

Your input: convert $$$\frac{600}{48}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{1}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\48&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}6&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$48$$$'s are in $$$6$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$6-48 \cdot 0 = 6 - 0= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{Brown}{0}&\phantom{1}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{48}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{Brown}{6}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$48$$$'s are in $$$60$$$?

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$60-48 \cdot 1 = 60 - 48= 12$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&\color{DarkMagenta}{1}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{48}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}6&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkMagenta}{6}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}4&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$48$$$'s are in $$$120$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$120-48 \cdot 2 = 120 - 96= 24$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&1&\color{DarkBlue}{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{48}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}6&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}4&8&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{1}&\color{DarkBlue}{2}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&2&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$48$$$'s are in $$$240$$$?

The answer is $$$5$$$.

Write down $$$5$$$ in the upper part of the table.

Now, $$$240-48 \cdot 5 = 240 - 240= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&1&2&.&\color{Purple}{5}\end{array}&\\\color{Magenta}{48}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}6&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}4&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&\color{Purple}{2}&\color{Purple}{4}&\phantom{.}&\color{Purple}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&4&\phantom{.}&0\\\hline\phantom{lll}&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{600}{48}=12.5 \overline{}$$$

Answer: $$$\frac{600}{48}=12.5\overline{}$$$