Υπολογιστής μετατροπής κλάσματος σε δεκαδικό

Your input: convert $$$\frac{1700}{40}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{4}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\40&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&7&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$40$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-40 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Blue}{0}&\phantom{0}&\phantom{4}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Blue}{1}& 7 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$40$$$'s are in $$$17$$$?

The answer is $$$0$$$.

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

Now, $$$17-40 \cdot 0 = 17 - 0= 17$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Fuchsia}{0}&\phantom{4}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&7& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Fuchsia}{1}&\color{Fuchsia}{7}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$40$$$'s are in $$$170$$$?

The answer is $$$4$$$.

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

Now, $$$170-40 \cdot 4 = 170 - 160= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{OrangeRed}{4}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&7&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{OrangeRed}{1}&\color{OrangeRed}{7}&\color{OrangeRed}{0}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$40$$$'s are in $$$100$$$?

The answer is $$$2$$$.

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

Now, $$$100-40 \cdot 2 = 100 - 80= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&4&\color{Purple}{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&7&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&0&\phantom{.}\\\hline\phantom{lll}&\color{Purple}{1}&\color{Purple}{0}&\color{Purple}{0}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&8&0&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$40$$$'s are in $$$200$$$?

The answer is $$$5$$$.

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

Now, $$$200-40 \cdot 5 = 200 - 200= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&4&2&.&\color{Chocolate}{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&7&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&8&0&\phantom{.}\\\hline\phantom{lll}&&\color{Chocolate}{2}&\color{Chocolate}{0}&\phantom{.}&\color{Chocolate}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&2&0&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{1700}{40}=42.5$$$

Answer: $$$\frac{1700}{40}=42.5$$$