分数转小数计算器

Your input: convert $$$\frac{500}{16}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{3}&\phantom{1}&\phantom{.}&\phantom{2}&\phantom{5}\end{array}&\\16&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}5&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$16$$$'s are in $$$5$$$?

The answer is $$$0$$$.

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

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

Bring down the next digit of the dividend.

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

Step 2

How many $$$16$$$'s are in $$$50$$$?

The answer is $$$3$$$.

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

Now, $$$50-16 \cdot 3 = 50 - 48= 2$$$.

Bring down the next digit of the dividend.

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

Step 3

How many $$$16$$$'s are in $$$20$$$?

The answer is $$$1$$$.

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

Now, $$$20-16 \cdot 1 = 20 - 16= 4$$$.

Bring down the next digit of the dividend.

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

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.

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

Step 5

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

The answer is $$$5$$$.

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

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

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

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

Therefore, $$$\frac{500}{16}=31.25$$$

Answer: $$$\frac{500}{16}=31.25$$$