分數轉小數計算器

Your input: convert $$$\frac{900}{16}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{5}&\phantom{6}&\phantom{.}&\phantom{2}&\phantom{5}\end{array}&\\16&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}9&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$16$$$'s are in $$$9$$$?

The answer is $$$0$$$.

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

Now, $$$9-16 \cdot 0 = 9 - 0= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Brown}{0}&\phantom{5}&\phantom{6}&\phantom{.}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Brown}{9}& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$16$$$'s are in $$$90$$$?

The answer is $$$5$$$.

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

Now, $$$90-16 \cdot 5 = 90 - 80= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{DarkMagenta}{5}&\phantom{6}&\phantom{.}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkMagenta}{9}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}8&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$16$$$'s are in $$$100$$$?

The answer is $$$6$$$.

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

Now, $$$100-16 \cdot 6 = 100 - 96= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&5&\color{DarkBlue}{6}&\phantom{.}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}8&0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{1}&\color{DarkBlue}{0}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$16$$$'s are in $$$40$$$?

The answer is $$$2$$$.

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

Now, $$$40-16 \cdot 2 = 40 - 32= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&5&6&.&\color{Purple}{2}&\phantom{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}8&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{4}&\phantom{.}&\color{Purple}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&2\\\hline\phantom{lll}&&&&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$16$$$'s are in $$$80$$$?

The answer is $$$5$$$.

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

Now, $$$80-16 \cdot 5 = 80 - 80= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&5&6&.&2&\color{DarkCyan}{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&0&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}8&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&2\\\hline\phantom{lll}&&&&\color{DarkCyan}{8}&\color{DarkCyan}{0}\\&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&8&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{900}{16}=56.25$$$

Answer: $$$\frac{900}{16}=56.25$$$