Calculadora de fracción a decimal

Convertir fracciones en decimales paso a paso

La calculadora convertirá la fracción dada (propia o impropia) o el número mixto en un decimal (posiblemente, periódico o repetido), mostrando los pasos.

Enter a fraction or

If you don't need a mixed number, leave the left cell empty.
If you need a negative fraction, write the minus sign in the left cell.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: convert $$$\frac{400}{7}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{5}&\phantom{7}&\phantom{.}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\7&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}4&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$7$$$'s are in $$$4$$$?

The answer is $$$0$$$.

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

Now, $$$4-7 \cdot 0 = 4 - 0= 4$$$.

Bring down the next digit of the dividend.

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

Step 2

How many $$$7$$$'s are in $$$40$$$?

The answer is $$$5$$$.

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

Now, $$$40-7 \cdot 5 = 40 - 35= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&\color{Peru}{5}&\phantom{7}&\phantom{.}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0& 0 \downarrow&.&0&0&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{4}&\color{Peru}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$7$$$'s are in $$$50$$$?

The answer is $$$7$$$.

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

Now, $$$50-7 \cdot 7 = 50 - 49= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&\color{Brown}{7}&\phantom{.}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.& 0 \downarrow&0&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&\color{Brown}{5}&\color{Brown}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$7$$$'s are in $$$10$$$?

The answer is $$$1$$$.

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

Now, $$$10-7 \cdot 1 = 10 - 7= 3$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&\color{DarkMagenta}{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0& 0 \downarrow&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&\color{DarkMagenta}{1}&\phantom{.}&\color{DarkMagenta}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$7$$$'s are in $$$30$$$?

The answer is $$$4$$$.

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

Now, $$$30-7 \cdot 4 = 30 - 28= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&1&\color{OrangeRed}{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0&0& 0 \downarrow&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&\color{OrangeRed}{3}&\color{OrangeRed}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&8\\\hline\phantom{lll}&&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$7$$$'s are in $$$20$$$?

The answer is $$$2$$$.

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

Now, $$$20-7 \cdot 2 = 20 - 14= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&1&4&\color{Green}{2}&\phantom{8}&\phantom{5}&\phantom{7}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0&0&0& 0 \downarrow&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&8\\\hline\phantom{lll}&&&&&\color{Green}{2}&\color{Green}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4\\\hline\phantom{lll}&&&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$7$$$'s are in $$$60$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$60-7 \cdot 8 = 60 - 56= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&1&4&2&\color{BlueViolet}{8}&\phantom{5}&\phantom{7}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0&0&0&0& 0 \downarrow&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&8\\\hline\phantom{lll}&&&&&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4\\\hline\phantom{lll}&&&&&&\color{BlueViolet}{6}&\color{BlueViolet}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&6\\\hline\phantom{lll}&&&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$7$$$'s are in $$$40$$$?

The answer is $$$5$$$.

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

Now, $$$40-7 \cdot 5 = 40 - 35= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&1&4&2&8&\color{Fuchsia}{5}&\phantom{7}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0&0&0&0&0& 0 \downarrow&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&8\\\hline\phantom{lll}&&&&&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4\\\hline\phantom{lll}&&&&&&6&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&6\\\hline\phantom{lll}&&&&&&&\color{Fuchsia}{4}&\color{Fuchsia}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 9

How many $$$7$$$'s are in $$$50$$$?

The answer is $$$7$$$.

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

Now, $$$50-7 \cdot 7 = 50 - 49= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&1&4&2&8&5&\color{GoldenRod}{7}&\phantom{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0&0&0&0&0&0& 0 \downarrow&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&8\\\hline\phantom{lll}&&&&&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4\\\hline\phantom{lll}&&&&&&6&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&6\\\hline\phantom{lll}&&&&&&&4&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&\color{GoldenRod}{5}&\color{GoldenRod}{0}\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&4&9\\\hline\phantom{lll}&&&&&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 10

How many $$$7$$$'s are in $$$10$$$?

The answer is $$$1$$$.

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

Now, $$$10-7 \cdot 1 = 10 - 7= 3$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&1&4&2&8&5&7&\color{DarkCyan}{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0&0&0&0&0&0&0& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&8\\\hline\phantom{lll}&&&&&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4\\\hline\phantom{lll}&&&&&&6&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&6\\\hline\phantom{lll}&&&&&&&4&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&5&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&4&9\\\hline\phantom{lll}&&&&&&&&&\color{DarkCyan}{1}&\color{DarkCyan}{0}\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&7\\\hline\phantom{lll}&&&&&&&&&&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 11

How many $$$7$$$'s are in $$$30$$$?

The answer is $$$4$$$.

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

Now, $$$30-7 \cdot 4 = 30 - 28= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&1&4&2&8&5&7&1&\color{Chocolate}{4}&\phantom{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0&0&0&0&0&0&0&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&8\\\hline\phantom{lll}&&&&&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4\\\hline\phantom{lll}&&&&&&6&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&6\\\hline\phantom{lll}&&&&&&&4&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&5&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&4&9\\\hline\phantom{lll}&&&&&&&&&1&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&7\\\hline\phantom{lll}&&&&&&&&&&\color{Chocolate}{3}&\color{Chocolate}{0}\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&2&8\\\hline\phantom{lll}&&&&&&&&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 12

How many $$$7$$$'s are in $$$20$$$?

The answer is $$$2$$$.

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

Now, $$$20-7 \cdot 2 = 20 - 14= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&1&4&2&8&5&7&1&4&\color{Red}{2}&\phantom{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0&0&0&0&0&0&0&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&8\\\hline\phantom{lll}&&&&&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4\\\hline\phantom{lll}&&&&&&6&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&6\\\hline\phantom{lll}&&&&&&&4&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&5&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&4&9\\\hline\phantom{lll}&&&&&&&&&1&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&7\\\hline\phantom{lll}&&&&&&&&&&3&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&2&8\\\hline\phantom{lll}&&&&&&&&&&&\color{Red}{2}&\color{Red}{0}\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&1&4\\\hline\phantom{lll}&&&&&&&&&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 13

How many $$$7$$$'s are in $$$60$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$60-7 \cdot 8 = 60 - 56= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&1&4&2&8&5&7&1&4&2&\color{Violet}{8}&\phantom{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0&0&0&0&0&0&0&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&8\\\hline\phantom{lll}&&&&&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4\\\hline\phantom{lll}&&&&&&6&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&6\\\hline\phantom{lll}&&&&&&&4&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&5&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&4&9\\\hline\phantom{lll}&&&&&&&&&1&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&7\\\hline\phantom{lll}&&&&&&&&&&3&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&2&8\\\hline\phantom{lll}&&&&&&&&&&&2&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&1&4\\\hline\phantom{lll}&&&&&&&&&&&&\color{Violet}{6}&\color{Violet}{0}\\&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&5&6\\\hline\phantom{lll}&&&&&&&&&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 14

How many $$$7$$$'s are in $$$40$$$?

The answer is $$$5$$$.

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

Now, $$$40-7 \cdot 5 = 40 - 35= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&1&4&2&8&5&7&1&4&2&8&\color{SaddleBrown}{5}&\phantom{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0&0&0&0&0&0&0&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&8\\\hline\phantom{lll}&&&&&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4\\\hline\phantom{lll}&&&&&&6&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&6\\\hline\phantom{lll}&&&&&&&4&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&5&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&4&9\\\hline\phantom{lll}&&&&&&&&&1&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&7\\\hline\phantom{lll}&&&&&&&&&&3&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&2&8\\\hline\phantom{lll}&&&&&&&&&&&2&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&1&4\\\hline\phantom{lll}&&&&&&&&&&&&6&0\\&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&5&6\\\hline\phantom{lll}&&&&&&&&&&&&&\color{SaddleBrown}{4}&\color{SaddleBrown}{0}\\&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&&&&&&&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 15

How many $$$7$$$'s are in $$$50$$$?

The answer is $$$7$$$.

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

Now, $$$50-7 \cdot 7 = 50 - 49= 1$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&5&7&.&1&4&2&8&5&7&1&4&2&8&5&\color{Crimson}{7}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}4&0&0&.&0&0&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&8\\\hline\phantom{lll}&&&&&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4\\\hline\phantom{lll}&&&&&&6&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&6\\\hline\phantom{lll}&&&&&&&4&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&5&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&4&9\\\hline\phantom{lll}&&&&&&&&&1&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&7\\\hline\phantom{lll}&&&&&&&&&&3&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&2&8\\\hline\phantom{lll}&&&&&&&&&&&2&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&1&4\\\hline\phantom{lll}&&&&&&&&&&&&6&0\\&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&5&6\\\hline\phantom{lll}&&&&&&&&&&&&&4&0\\&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&&&&&&&\color{Crimson}{5}&\color{Crimson}{0}\\&&&&&&&&&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&&4&9\\\hline\phantom{lll}&&&&&&&&&&&&&&&1\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: $$$\frac{400}{7}=57. \overline{142857}$$$

Answer: $$$\frac{400}{7}=57.\overline{142857}$$$


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