分数转小数计算器

Your input: convert $$$\frac{100}{32}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{3}&\phantom{.}&\phantom{1}&\phantom{2}&\phantom{5}\end{array}&\\32&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}1&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$32$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-32 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Red}{0}&\phantom{0}&\phantom{3}&\phantom{.}&\phantom{1}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Red}{1}& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$32$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-32 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Crimson}{0}&\phantom{3}&\phantom{.}&\phantom{1}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Crimson}{1}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$32$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-32 \cdot 3 = 100 - 96= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{Chartreuse}{3}&\phantom{.}&\phantom{1}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{1}&\color{Chartreuse}{0}&\color{Chartreuse}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$32$$$'s are in $$$40$$$?

The answer is $$$1$$$.

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

Now, $$$40-32 \cdot 1 = 40 - 32= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&3&.&\color{BlueViolet}{1}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&\color{BlueViolet}{4}&\phantom{.}&\color{BlueViolet}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&2\\\hline\phantom{lll}&&&&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$32$$$'s are in $$$80$$$?

The answer is $$$2$$$.

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

Now, $$$80-32 \cdot 2 = 80 - 64= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&3&.&1&\color{DarkCyan}{2}&\phantom{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&2\\\hline\phantom{lll}&&&&\color{DarkCyan}{8}&\color{DarkCyan}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&6&4\\\hline\phantom{lll}&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$32$$$'s are in $$$160$$$?

The answer is $$$5$$$.

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

Now, $$$160-32 \cdot 5 = 160 - 160= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&3&.&1&2&\color{DarkMagenta}{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&2\\\hline\phantom{lll}&&&&8&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&6&4\\\hline\phantom{lll}&&&&\color{DarkMagenta}{1}&\color{DarkMagenta}{6}&\color{DarkMagenta}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&6&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Since the remainder is $$$0$$$, then we are done.

Therefore, $$$\frac{100}{32}=3.125$$$

Answer: $$$\frac{100}{32}=3.125$$$