Fraction to Decimal Calculator

The calculator will convert the given fraction (proper or improper) or mixed number into decimal (repeating or recurring), with steps shown.

Show Instructions
  • In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`.
  • In general, you can skip parentheses, but be very careful: e^3x is `e^3x`, and e^(3x) is `e^(3x)`.
  • Also, be careful when you write fractions: 1/x^2 ln(x) is `1/x^2 ln(x)`, and 1/(x^2 ln(x)) is `1/(x^2 ln(x))`.
  • If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. write sin x (or even better sin(x)) instead of sinx.
  • Sometimes I see expressions like tan^2xsec^3x: this will be parsed as `tan^(2*3)(x sec(x))`. To get `tan^2(x)sec^3(x)`, use parentheses: tan^2(x)sec^3(x).
  • Similarly, tanxsec^3x will be parsed as `tan(xsec^3(x))`. To get `tan(x)sec^3(x)`, use parentheses: tan(x)sec^3(x).
  • From the table below, you can notice that sech is not supported, but you can still enter it using the identity `sech(x)=1/cosh(x)`.
  • If you get an error, double check your expression, add parentheses and multiplication signs where needed, and consult the table below.
  • All suggestions and improvements are welcome. Please leave them in comments.
The following table contains the supported operations and functions:
TypeGet
Constants
ee
pi`pi`
ii (imaginary unit)
Operations
a+ba+b
a-ba-b
a*b`a*b`
a^b, a**b`a^b`
sqrt(x), x^(1/2)`sqrt(x)`
cbrt(x), x^(1/3)`root(3)(x)`
root(x,n), x^(1/n)`root(n)(x)`
x^(a/b)`x^(a/b)`
abs(x)`|x|`
Functions
e^x`e^x`
ln(x), log(x)ln(x)
ln(x)/ln(a)`log_a(x)`
Trigonometric Functions
sin(x)sin(x)
cos(x)cos(x)
tan(x)tan(x), tg(x)
cot(x)cot(x), ctg(x)
sec(x)sec(x)
csc(x)csc(x), cosec(x)
Inverse Trigonometric Functions
asin(x), arcsin(x), sin^-1(x)asin(x)
acos(x), arccos(x), cos^-1(x)acos(x)
atan(x), arctan(x), tan^-1(x)atan(x)
acot(x), arccot(x), cot^-1(x)acot(x)
asec(x), arcsec(x), sec^-1(x)asec(x)
acsc(x), arccsc(x), csc^-1(x)acsc(x)
Hyperbolic Functions
sinh(x)sinh(x)
cosh(x)cosh(x)
tanh(x)tanh(x)
coth(x)coth(x)
1/cosh(x)sech(x)
1/sinh(x)csch(x)
Inverse Hyperbolic Functions
asinh(x), arcsinh(x), sinh^-1(x)asinh(x)
acosh(x), arccosh(x), cosh^-1(x)acosh(x)
atanh(x), arctanh(x), tanh^-1(x)atanh(x)
acoth(x), arccoth(x), cot^-1(x)acoth(x)
acosh(1/x)asech(x)
asinh(1/x)acsch(x)

Enter a fraction or

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

Write all suggestions in comments below.

Solution

Your input: convert $$$2\frac{5}{7}$$$ into decimal.

Temporarily forget about the integer part, work with $$$\frac{5}{7}$$$

Write the problem in a special format:

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

Step 1

How many $$$7$$$'s are in $$$5$$$? The answer is $$$0$$$.

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

Now, $$$5-0 \cdot 7 = 5 - 0= 5$$$.

Bring down the next digit of the dividend.

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

Step 2

How many $$$7$$$'s are in $$$50$$$? The answer is $$$7$$$.

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

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

Bring down the next digit of the dividend.

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

Step 3

How many $$$7$$$'s are in $$$10$$$? The answer is $$$1$$$.

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

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

Bring down the next digit of the dividend.

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

Step 4

How many $$$7$$$'s are in $$$30$$$? The answer is $$$4$$$.

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

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

Bring down the next digit of the dividend.

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

Step 5

How many $$$7$$$'s are in $$$20$$$? The answer is $$$2$$$.

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

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

Bring down the next digit of the dividend.

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

Step 6

How many $$$7$$$'s are in $$$60$$$? The answer is $$$8$$$.

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

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

Bring down the next digit of the dividend.

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

Step 7

How many $$$7$$$'s are in $$$40$$$? The answer is $$$5$$$.

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

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

Bring down the next digit of the dividend.

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

Step 8

How many $$$7$$$'s are in $$$50$$$? The answer is $$$7$$$.

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

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

Bring down the next digit of the dividend.

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

Step 9

How many $$$7$$$'s are in $$$10$$$? The answer is $$$1$$$.

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

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

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccc}0&.&7&1&4&2&8&5&7&\color{GoldenRod}{1}&\phantom{4}&\phantom{2}&\phantom{8}&\phantom{5}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccc}5&.&0&0&0&0&0&0&0&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllllllll}-&\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}5&\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}4&\phantom{.}&9\\\hline\phantom{lll}&&1&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}&&&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{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{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{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{lll}&&&&&&3&5\\\hline\phantom{lll}&&&&&&&5&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&4&9\\\hline\phantom{lll}&&&&&&&&\color{GoldenRod}{1}&\color{GoldenRod}{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 10

How many $$$7$$$'s are in $$$30$$$? The answer is $$$4$$$.

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

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

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccc}0&.&7&1&4&2&8&5&7&1&\color{DarkCyan}{4}&\phantom{2}&\phantom{8}&\phantom{5}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccc}5&.&0&0&0&0&0&0&0&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllllllll}-&\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}5&\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}4&\phantom{.}&9\\\hline\phantom{lll}&&1&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}&&&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{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{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{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{lll}&&&&&&3&5\\\hline\phantom{lll}&&&&&&&5&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{lll}&&&&&&&&&7\\\hline\phantom{lll}&&&&&&&&&\color{DarkCyan}{3}&\color{DarkCyan}{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 11

How many $$$7$$$'s are in $$$20$$$? The answer is $$$2$$$.

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

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

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccc}0&.&7&1&4&2&8&5&7&1&4&\color{Crimson}{2}&\phantom{8}&\phantom{5}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccc}5&.&0&0&0&0&0&0&0&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllllllll}-&\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}5&\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}4&\phantom{.}&9\\\hline\phantom{lll}&&1&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}&&&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{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{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{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{lll}&&&&&&3&5\\\hline\phantom{lll}&&&&&&&5&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{lll}&&&&&&&&&7\\\hline\phantom{lll}&&&&&&&&&3&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&2&8\\\hline\phantom{lll}&&&&&&&&&&\color{Crimson}{2}&\color{Crimson}{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 12

How many $$$7$$$'s are in $$$60$$$? The answer is $$$8$$$.

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

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

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccc}0&.&7&1&4&2&8&5&7&1&4&2&\color{SaddleBrown}{8}&\phantom{5}\end{array}&\\\color{Magenta}{7}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccc}5&.&0&0&0&0&0&0&0&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllllllll}-&\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}5&\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}4&\phantom{.}&9\\\hline\phantom{lll}&&1&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}&&&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{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{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{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{lll}&&&&&&3&5\\\hline\phantom{lll}&&&&&&&5&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{lll}&&&&&&&&&7\\\hline\phantom{lll}&&&&&&&&&3&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{lll}&&&&&&&&&&1&4\\\hline\phantom{lll}&&&&&&&&&&&\color{SaddleBrown}{6}&\color{SaddleBrown}{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 13

How many $$$7$$$'s are in $$$40$$$? The answer is $$$5$$$.

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

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

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

As can be seen, digits are repeating with some period, therefore it is a repeating (or recurring decimal): $$$\frac{5}{7}=0. \overline{714285}$$$

Don't forget about the integer part: $$$2\frac{5}{7}=2.\overline{714285}$$$

Answer: $$$2\frac{5}{7}=2.\overline{714285}$$$