# 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.

• 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:
 Type Get Constants e e pi pi i i (imaginary unit) Operations a+b a+b a-b a-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: $$2\frac{5}{7}=2.\overline{714285}$$\$