Υπολογιστής μετατροπής κλάσματος σε δεκαδικό

Your input: convert $$$\frac{14500}{200}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\phantom{7}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\200&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}1&4&5&0&0\end{array}}&\\&\begin{array}{lllll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$200$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-200 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Green}{0}&\phantom{0}&\phantom{0}&\phantom{7}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Green}{1}& 4 \downarrow&5&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$200$$$'s are in $$$14$$$?

The answer is $$$0$$$.

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

Now, $$$14-200 \cdot 0 = 14 - 0= 14$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Chocolate}{0}&\phantom{0}&\phantom{7}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&4& 5 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{4}&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&4&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$200$$$'s are in $$$145$$$?

The answer is $$$0$$$.

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

Now, $$$145-200 \cdot 0 = 145 - 0= 145$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{GoldenRod}{0}&\phantom{7}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&4&5& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{GoldenRod}{1}&\color{GoldenRod}{4}&\color{GoldenRod}{5}&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&4&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$200$$$'s are in $$$1450$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$1450-200 \cdot 7 = 1450 - 1400= 50$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&\color{Purple}{7}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&4&5&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&4&5&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{4}&\color{Purple}{5}&\color{Purple}{0}&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&0&0&\phantom{.}\\\hline\phantom{lll}&&5&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$200$$$'s are in $$$500$$$?

The answer is $$$2$$$.

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

Now, $$$500-200 \cdot 2 = 500 - 400= 100$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&7&\color{DarkMagenta}{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&4&5&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&4&5&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&4&5&0&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&0&0&\phantom{.}\\\hline\phantom{lll}&&\color{DarkMagenta}{5}&\color{DarkMagenta}{0}&\color{DarkMagenta}{0}&\phantom{.}\\&-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&4&0&0&\phantom{.}\\\hline\phantom{lll}&&1&0&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

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

The answer is $$$5$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&7&2&.&\color{SaddleBrown}{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&4&5&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&4&5&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&4&5&0&\phantom{.}\\-&\phantom{4}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&0&0&\phantom{.}\\\hline\phantom{lll}&&5&0&0&\phantom{.}\\&-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&4&0&0&\phantom{.}\\\hline\phantom{lll}&&\color{SaddleBrown}{1}&\color{SaddleBrown}{0}&\color{SaddleBrown}{0}&\phantom{.}&\color{SaddleBrown}{0}\\&-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&1&0&0&\phantom{.}&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{14500}{200}=72.5$$$

Answer: $$$\frac{14500}{200}=72.5$$$