分数转小数计算器

Your input: convert $$$\frac{1800}{24}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\24&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&8&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$24$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-24 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Violet}{0}&\phantom{0}&\phantom{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Violet}{1}& 8 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$24$$$'s are in $$$18$$$?

The answer is $$$0$$$.

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

Now, $$$18-24 \cdot 0 = 18 - 0= 18$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Purple}{0}&\phantom{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{8}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$24$$$'s are in $$$180$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$180-24 \cdot 7 = 180 - 168= 12$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Blue}{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Blue}{1}&\color{Blue}{8}&\color{Blue}{0}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&8&\phantom{.}\\\hline\phantom{lll}&1&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$24$$$'s are in $$$120$$$?

The answer is $$$5$$$.

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

Now, $$$120-24 \cdot 5 = 120 - 120= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&7&\color{DeepPink}{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&8&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&8&\phantom{.}\\\hline\phantom{lll}&\color{DeepPink}{1}&\color{DeepPink}{2}&\color{DeepPink}{0}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&2&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$24$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-24 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&7&5&.&\color{GoldenRod}{0}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&8&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&8&\phantom{.}\\\hline\phantom{lll}&1&2&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&2&0&\phantom{.}\\\hline\phantom{lll}&&&\color{GoldenRod}{0}&\phantom{.}&\color{GoldenRod}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1800}{24}=75.0 \overline{}$$$

Answer: $$$\frac{1800}{24}=75.0\overline{}$$$