分数转小数计算器

Your input: convert $$$\frac{1900}{30}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{6}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\30&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&9&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$30$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-30 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Red}{0}&\phantom{0}&\phantom{6}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Red}{1}& 9 \downarrow&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&9&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$30$$$'s are in $$$19$$$?

The answer is $$$0$$$.

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

Now, $$$19-30 \cdot 0 = 19 - 0= 19$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Crimson}{0}&\phantom{6}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&9& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Crimson}{1}&\color{Crimson}{9}&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$30$$$'s are in $$$190$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$190-30 \cdot 6 = 190 - 180= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{Blue}{6}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&9&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Blue}{1}&\color{Blue}{9}&\color{Blue}{0}&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$30$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-30 \cdot 3 = 100 - 90= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&6&\color{Chocolate}{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&9&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&9&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&\color{Chocolate}{1}&\color{Chocolate}{0}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$30$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-30 \cdot 3 = 100 - 90= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&6&3&.&\color{Purple}{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&9&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&9&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&0&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{1}&\color{Purple}{0}&\phantom{.}&\color{Purple}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9&0\\\hline\phantom{lll}&&&1&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$30$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-30 \cdot 3 = 100 - 90= 10$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&6&3&.&3&\color{OrangeRed}{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&9&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&9&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9&0\\\hline\phantom{lll}&&&\color{OrangeRed}{1}&\phantom{.}&\color{OrangeRed}{0}&\color{OrangeRed}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&9&\phantom{.}&0\\\hline\phantom{lll}&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1900}{30}=63. \overline{3}$$$

Answer: $$$\frac{1900}{30}=63.\overline{3}$$$