Fraction to Decimal Calculator

Your input: convert $$$\frac{700}{22}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{3}&\phantom{1}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}\end{array}&\\22&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}7&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$22$$$'s are in $$$7$$$? The answer is $$$0$$$.

Write down the calculated result in the upper part of the table.

Now, $$$7-0 \cdot 22 = 7 - 0= 7$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}\color{DarkCyan}{0}&\phantom{3}&\phantom{1}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}\color{DarkCyan}{7}& 0 \downarrow&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$22$$$'s are in $$$70$$$? The answer is $$$3$$$.

Write down the calculated result in the upper part of the table.

Now, $$$70-3 \cdot 22 = 70 - 66= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&\color{Peru}{3}&\phantom{1}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}7&0& 0 \downarrow&.&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{7}&\color{Peru}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&6&\phantom{.}\\\hline\phantom{lll}&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$22$$$'s are in $$$40$$$? The answer is $$$1$$$.

Write down the calculated result in the upper part of the table.

Now, $$$40-1 \cdot 22 = 40 - 22= 18$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&3&\color{Red}{1}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}7&0&0&.& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&6&\phantom{.}\\\hline\phantom{lll}&\color{Red}{4}&\color{Red}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&2&\phantom{.}\\\hline\phantom{lll}&1&8&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$22$$$'s are in $$$180$$$? The answer is $$$8$$$.

Write down the calculated result in the upper part of the table.

Now, $$$180-8 \cdot 22 = 180 - 176= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&3&1&.&\color{Chartreuse}{8}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}7&0&0&.&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&6&\phantom{.}\\\hline\phantom{lll}&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&2&\phantom{.}\\\hline\phantom{lll}&\color{Chartreuse}{1}&\color{Chartreuse}{8}&\phantom{.}&\color{Chartreuse}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&7&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$22$$$'s are in $$$40$$$? The answer is $$$1$$$.

Write down the calculated result in the upper part of the table.

Now, $$$40-1 \cdot 22 = 40 - 22= 18$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&3&1&.&8&\color{Chocolate}{1}&\phantom{8}&\phantom{1}&\phantom{8}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}7&0&0&.&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&6&\phantom{.}\\\hline\phantom{lll}&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&2&\phantom{.}\\\hline\phantom{lll}&1&8&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&7&\phantom{.}&6\\\hline\phantom{lll}&&&&\color{Chocolate}{4}&\color{Chocolate}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&2\\\hline\phantom{lll}&&&&1&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$22$$$'s are in $$$180$$$? The answer is $$$8$$$.

Write down the calculated result in the upper part of the table.

Now, $$$180-8 \cdot 22 = 180 - 176= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&3&1&.&8&1&\color{OrangeRed}{8}&\phantom{1}&\phantom{8}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}7&0&0&.&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&6&\phantom{.}\\\hline\phantom{lll}&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&2&\phantom{.}\\\hline\phantom{lll}&1&8&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&7&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&2\\\hline\phantom{lll}&&&&\color{OrangeRed}{1}&\color{OrangeRed}{8}&\color{OrangeRed}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&7&6\\\hline\phantom{lll}&&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$22$$$'s are in $$$40$$$? The answer is $$$1$$$.

Write down the calculated result in the upper part of the table.

Now, $$$40-1 \cdot 22 = 40 - 22= 18$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&3&1&.&8&1&8&\color{DeepPink}{1}&\phantom{8}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}7&0&0&.&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&6&\phantom{.}\\\hline\phantom{lll}&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&2&\phantom{.}\\\hline\phantom{lll}&1&8&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&7&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&2\\\hline\phantom{lll}&&&&1&8&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&7&6\\\hline\phantom{lll}&&&&&&\color{DeepPink}{4}&\color{DeepPink}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&2&2\\\hline\phantom{lll}&&&&&&1&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$22$$$'s are in $$$180$$$? The answer is $$$8$$$.

Write down the calculated result in the upper part of the table.

Now, $$$180-8 \cdot 22 = 180 - 176= 4$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&3&1&.&8&1&8&1&\color{Fuchsia}{8}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}7&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&6&\phantom{.}\\\hline\phantom{lll}&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&2&\phantom{.}\\\hline\phantom{lll}&1&8&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&7&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&2\\\hline\phantom{lll}&&&&1&8&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&7&6\\\hline\phantom{lll}&&&&&&4&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&2&2\\\hline\phantom{lll}&&&&&&\color{Fuchsia}{1}&\color{Fuchsia}{8}&\color{Fuchsia}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&1&7&6\\\hline\phantom{lll}&&&&&&&&4\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{700}{22}=31.8 \overline{18}$$$

Answer: $$$\frac{700}{22}=31.8\overline{18}$$$