Murtoluvusta desimaaliluvuksi -laskin

Your input: convert $$$\frac{9000}{200}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{4}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\200&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}9&0&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$200$$$'s are in $$$9$$$?

The answer is $$$0$$$.

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

Now, $$$9-200 \cdot 0 = 9 - 0= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{DarkMagenta}{0}&\phantom{0}&\phantom{4}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{DarkMagenta}{9}& 0 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$200$$$'s are in $$$90$$$?

The answer is $$$0$$$.

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

Now, $$$90-200 \cdot 0 = 90 - 0= 90$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{OrangeRed}{0}&\phantom{4}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&0& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{OrangeRed}{9}&\color{OrangeRed}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}9&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$200$$$'s are in $$$900$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

Now, $$$900-200 \cdot 4 = 900 - 800= 100$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{DarkCyan}{4}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&0&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DarkCyan}{9}&\color{DarkCyan}{0}&\color{DarkCyan}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}8&0&0&\phantom{.}\\\hline\phantom{lll}1&0&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$200$$$'s are in $$$1000$$$?

The answer is $$$5$$$.

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

Now, $$$1000-200 \cdot 5 = 1000 - 1000= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&4&\color{GoldenRod}{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&0&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}9&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}8&0&0&\phantom{.}\\\hline\phantom{lll}\color{GoldenRod}{1}&\color{GoldenRod}{0}&\color{GoldenRod}{0}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$200$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-200 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&4&5&.&\color{Violet}{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&0&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}9&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}8&0&0&\phantom{.}\\\hline\phantom{lll}1&0&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&0&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Violet}{0}&\phantom{.}&\color{Violet}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{9000}{200}=45.0$$$

Answer: $$$\frac{9000}{200}=45.0$$$