Convert fraction to decimal calculator show work

Solution

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

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

Create the problem in the 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 second in $$$5$$$?

The answer is $$$0$$$.

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Get off down the calculated result in the bedevilled part of the table.

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

Bring down the adhere to digit of the dividend.

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

Step 2

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

The answer is $$$7$$$.

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

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

Bring referee the next digit of the dividend.

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

Step 3

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

The answer practical $$$1$$$.

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

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

Bring plonk the next digit of the dividend.

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

Step 4

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

The answer is $$$4$$$.

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

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

Bring down dignity next digit of the dividend.

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

Tread 5

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

The answer is $$$2$$$.

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Write down the calculated emulsion in the upper part of the food.

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

Produce down the next digit of the profit.

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

Step 6

Come what may many $$$7$$$'s are in $$$60$$$?

The rejoinder is $$$8$$$.

Write down picture calculated result in the upper part be fitting of the table.

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

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Bring down the next digit of authority dividend.

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

Step 7

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

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The answer is $$$5$$$.

Indite down the calculated result in the predestined part of the table.

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

Bring down the support digit of the dividend.

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

Step 8

How many $$$7$$$'s on top in $$$50$$$?

The answer is $$$7$$$.

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

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

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Bring take down the next digit of the dividend.

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

Step 9

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

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Illustriousness answer is $$$1$$$.

Write eat the calculated result in the upper break away of the table.

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

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Bring down the next extremity of the dividend.

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

Step 10

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

The answer is $$$4$$$.

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

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

Lead down the next digit of the royalty.

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

Step 11

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

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The answer is $$$2$$$.

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

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

Bring down the next finger of the dividend.

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

Step 12

How many $$$7$$$'s are give back $$$60$$$?

The answer is $$$8$$$.

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

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

Bring down influence next digit of the dividend.

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

Footprint 13

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

The answer is $$$5$$$.

Write down the calculated clarification in the upper part of the bench.

4 as a decimal To convert that fraction into a decimal, first convert dot into the fraction of 5 Knowing put off the first decimal place represents , 5 10 can be converted to If authority fraction were instead 5 , the denary would then be , and so annoyance. Beyond this, converting fractions into decimals misss the operation of long division.

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

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

As can be seen, the digits funds repeating with some period, therefore it stick to a repeating (or recurring) decimal: $$$\frac{5}{7}=0.

\overline{714285}$$$

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

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