分数转小数计算器

Your input: convert $$$\frac{3100}{40}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{7}&\phantom{7}&\phantom{.}&\phantom{5}\end{array}&\\40&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}3&1&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$40$$$'s are in $$$3$$$?

The answer is $$$0$$$.

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

Now, $$$3-40 \cdot 0 = 3 - 0= 3$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Crimson}{0}&\phantom{0}&\phantom{7}&\phantom{7}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Crimson}{3}& 1 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&1&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$40$$$'s are in $$$31$$$?

The answer is $$$0$$$.

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

Now, $$$31-40 \cdot 0 = 31 - 0= 31$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{DarkBlue}{0}&\phantom{7}&\phantom{7}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&1& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{3}&\color{DarkBlue}{1}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$40$$$'s are in $$$310$$$?

The answer is $$$7$$$.

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

Now, $$$310-40 \cdot 7 = 310 - 280= 30$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{SaddleBrown}{7}&\phantom{7}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&1&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{3}&\color{SaddleBrown}{1}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&8&0&\phantom{.}\\\hline\phantom{lll}&3&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$40$$$'s are in $$$300$$$?

The answer is $$$7$$$.

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

Now, $$$300-40 \cdot 7 = 300 - 280= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&7&\color{Chocolate}{7}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&1&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&8&0&\phantom{.}\\\hline\phantom{lll}&\color{Chocolate}{3}&\color{Chocolate}{0}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&8&0&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

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

The answer is $$$5$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&7&7&.&\color{Blue}{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&1&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&8&0&\phantom{.}\\\hline\phantom{lll}&3&0&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&8&0&\phantom{.}\\\hline\phantom{lll}&&\color{Blue}{2}&\color{Blue}{0}&\phantom{.}&\color{Blue}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&2&0&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{3100}{40}=77.5$$$

Answer: $$$\frac{3100}{40}=77.5$$$