Murtoluvusta desimaaliluvuksi -laskin

Your input: convert $$$\frac{200}{16}$$$ into a decimal.

Write the problem in the special format:

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

Step 1

How many $$$16$$$'s are in $$$2$$$?

The answer is $$$0$$$.

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

Now, $$$2-16 \cdot 0 = 2 - 0= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{SaddleBrown}{0}&\phantom{1}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{SaddleBrown}{2}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&\color{Brown}{1}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}2&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Brown}{2}&\color{Brown}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&\phantom{.}\\\hline\phantom{lll}&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

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.

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

Step 4

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

The answer is $$$5$$$.

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

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

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

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

Therefore, $$$\frac{200}{16}=12.5$$$

Answer: $$$\frac{200}{16}=12.5$$$