分数转小数计算器

Your input: convert $$$\frac{5300}{60}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{8}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\60&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}5&3&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$60$$$'s are in $$$5$$$?

The answer is $$$0$$$.

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

Now, $$$5-60 \cdot 0 = 5 - 0= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Crimson}{0}&\phantom{0}&\phantom{8}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Crimson}{5}& 3 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&3&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$60$$$'s are in $$$53$$$?

The answer is $$$0$$$.

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

Now, $$$53-60 \cdot 0 = 53 - 0= 53$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{DarkBlue}{0}&\phantom{8}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&3& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{5}&\color{DarkBlue}{3}&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&3&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$60$$$'s are in $$$530$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$530-60 \cdot 8 = 530 - 480= 50$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{SaddleBrown}{8}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&3&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{5}&\color{SaddleBrown}{3}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}4&8&0&\phantom{.}\\\hline\phantom{lll}&5&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$60$$$'s are in $$$500$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$500-60 \cdot 8 = 500 - 480= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&\color{Chocolate}{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&3&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}4&8&0&\phantom{.}\\\hline\phantom{lll}&\color{Chocolate}{5}&\color{Chocolate}{0}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&8&0&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$60$$$'s are in $$$200$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$200-60 \cdot 3 = 200 - 180= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&8&.&\color{Blue}{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&3&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}4&8&0&\phantom{.}\\\hline\phantom{lll}&5&0&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&8&0&\phantom{.}\\\hline\phantom{lll}&&\color{Blue}{2}&\color{Blue}{0}&\phantom{.}&\color{Blue}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&8&\phantom{.}&0\\\hline\phantom{lll}&&&2&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$60$$$'s are in $$$200$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$200-60 \cdot 3 = 200 - 180= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&8&.&3&\color{DeepPink}{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&3&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}4&8&0&\phantom{.}\\\hline\phantom{lll}&5&0&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&8&0&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&8&\phantom{.}&0\\\hline\phantom{lll}&&&\color{DeepPink}{2}&\phantom{.}&\color{DeepPink}{0}&\color{DeepPink}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&8&0\\\hline\phantom{lll}&&&&&2&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$60$$$'s are in $$$200$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$200-60 \cdot 3 = 200 - 180= 20$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&8&.&3&3&\color{Green}{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&3&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}4&8&0&\phantom{.}\\\hline\phantom{lll}&5&0&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&8&0&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&8&\phantom{.}&0\\\hline\phantom{lll}&&&2&\phantom{.}&0&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&8&0\\\hline\phantom{lll}&&&&&\color{Green}{2}&\color{Green}{0}&\color{Green}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&8&0\\\hline\phantom{lll}&&&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{5300}{60}=88.3 \overline{3}$$$

Answer: $$$\frac{5300}{60}=88.3\overline{3}$$$