分數轉小數計算器

Your input: convert $$$\frac{4500}{40}$$$ into a decimal.

Write the problem in the special format:

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

Step 1

How many $$$40$$$'s are in $$$4$$$?

The answer is $$$0$$$.

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

Now, $$$4-40 \cdot 0 = 4 - 0= 4$$$.

Bring down the next digit of the dividend.

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

Step 2

How many $$$40$$$'s are in $$$45$$$?

The answer is $$$1$$$.

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

Now, $$$45-40 \cdot 1 = 45 - 40= 5$$$.

Bring down the next digit of the dividend.

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

Step 3

How many $$$40$$$'s are in $$$50$$$?

The answer is $$$1$$$.

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

Now, $$$50-40 \cdot 1 = 50 - 40= 10$$$.

Bring down the next digit of the dividend.

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

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.

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

Step 5

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

The answer is $$$5$$$.

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

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

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

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

Therefore, $$$\frac{4500}{40}=112.5$$$

Answer: $$$\frac{4500}{40}=112.5$$$