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Калькулятор переведення дробів у десяткові дроби

Покрокове перетворення дробів у десяткові

Калькулятор перетворить заданий дріб (правильний або неправильний) або мішане число в десятковий дріб (можливо, повторюваний або періодичний), з показаними кроками.

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 260035 into a decimal.

Write the problem in the special format:

74.2857142857142352600

Step 1

How many 35's are in 2? The answer is 0.

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

Now, 2035=20=2.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.

Step 2

How many 35's are in 26? The answer is 0.

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

Now, 26035=260=26.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.6000.000000000000lll0.lll260.

Step 3

How many 35's are in 260? The answer is 7.

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

Now, 260735=260245=15.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.6000.000000000000lll0.lll260.6000.000000000000lll245.lll150.

Step 4

How many 35's are in 150? The answer is 4.

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

Now, 150435=150140=10.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.6000.000000000000lll0.lll260.6000.000000000000lll245.lll150.600.0000000000000lll140.lll10.0

Step 5

How many 35's are in 100? The answer is 2.

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

Now, 100235=10070=30.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.6000.000000000000lll0.lll260.6000.000000000000lll245.lll150.600.0000000000000lll140.lll10.000.0000000000000lll.70lll3.00

Step 6

How many 35's are in 300? The answer is 8.

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

Now, 300835=300280=20.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.6000.000000000000lll0.lll260.6000.000000000000lll245.lll150.600.0000000000000lll140.lll10.000.0000000000000lll.70lll3.000.0000000000000lll2.80lll200

Step 7

How many 35's are in 200? The answer is 5.

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

Now, 200535=200175=25.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.6000.000000000000lll0.lll260.6000.000000000000lll245.lll150.600.0000000000000lll140.lll10.000.0000000000000lll.70lll3.000.0000000000000lll2.80lll2000000000000000lll175lll250

Step 8

How many 35's are in 250? The answer is 7.

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

Now, 250735=250245=5.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.6000.000000000000lll0.lll260.6000.000000000000lll245.lll150.600.0000000000000lll140.lll10.000.0000000000000lll.70lll3.000.0000000000000lll2.80lll2000000000000000lll175lll250000000000000lll245lll50

Step 9

How many 35's are in 50? The answer is 1.

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

Now, 50135=5035=15.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.6000.000000000000lll0.lll260.6000.000000000000lll245.lll150.600.0000000000000lll140.lll10.000.0000000000000lll.70lll3.000.0000000000000lll2.80lll2000000000000000lll175lll250000000000000lll245lll500000000000lll35lll150

Step 10

How many 35's are in 150? The answer is 4.

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

Now, 150435=150140=10.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.6000.000000000000lll0.lll260.6000.000000000000lll245.lll150.600.0000000000000lll140.lll10.000.0000000000000lll.70lll3.000.0000000000000lll2.80lll2000000000000000lll175lll250000000000000lll245lll500000000000lll35lll1500000000000lll140lll100

Step 11

How many 35's are in 100? The answer is 2.

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

Now, 100235=10070=30.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.6000.000000000000lll0.lll260.6000.000000000000lll245.lll150.600.0000000000000lll140.lll10.000.0000000000000lll.70lll3.000.0000000000000lll2.80lll2000000000000000lll175lll250000000000000lll245lll500000000000lll35lll1500000000000lll140lll100000000000lll70lll300

Step 12

How many 35's are in 300? The answer is 8.

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

Now, 300835=300280=20.

Bring down the next digit of the dividend.

0074.2857142857142352600.00000000000006000.000000000000lll0.lll26.6000.000000000000lll0.lll260.6000.000000000000lll245.lll150.600.0000000000000lll140.lll10.000.0000000000000lll.70lll3.000.0000000000000lll2.80lll2000000000000000lll175lll250000000000000lll245lll500000000000lll35lll1500000000000lll140lll100000000000lll70lll30000000000lll280lll200

Step 13

How many 35's are in 200? The answer is 5.

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

Now, 200-5 \cdot 35 = 200 - 175= 25.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccccc}0&0&7&4&.&2&8&5&7&1&4&2&8&\color{OrangeRed}{5}&\phantom{7}&\phantom{1}&\phantom{4}&\phantom{2}\end{array}&\\\color{Magenta}{35}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccccc}2&6&0&0&.&0&0&0&0&0&0&0&0&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllllll}-&\phantom{6}&\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{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&6&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&6&0&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}2&4&5&\phantom{.}\\\hline\phantom{lll}&1&5&0&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}&1&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\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{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7&0\\\hline\phantom{lll}&&&3&\phantom{.}&0&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{0}\\\phantom{lll}&&&2&\phantom{.}&8&0\\\hline\phantom{lll}&&&&&2&0&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{0}\\\phantom{lll}&&&&&1&7&5\\\hline\phantom{lll}&&&&&&2&5&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&4&5\\\hline\phantom{lll}&&&&&&&&5&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\\\hline\phantom{lll}&&&&&&&&1&5&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&0\\\hline\phantom{lll}&&&&&&&&&1&0&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&7&0\\\hline\phantom{lll}&&&&&&&&&&3&0&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&2&8&0\\\hline\phantom{lll}&&&&&&&&&&&\color{OrangeRed}{2}&\color{OrangeRed}{0}&\color{OrangeRed}{0}\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&1&7&5\\\hline\phantom{lll}&&&&&&&&&&&&2&5&0\end{array}&\begin{array}{c}\end{array}\end{array}

Step 14

How many 35's are in 250? The answer is 7.

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

Now, 250-7 \cdot 35 = 250 - 245= 5.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccccc}0&0&7&4&.&2&8&5&7&1&4&2&8&5&\color{DarkBlue}{7}&\phantom{1}&\phantom{4}&\phantom{2}\end{array}&\\\color{Magenta}{35}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccccc}2&6&0&0&.&0&0&0&0&0&0&0&0&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllllllllllll}-&\phantom{6}&\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{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&6&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&6&0&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}2&4&5&\phantom{.}\\\hline\phantom{lll}&1&5&0&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}&1&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\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{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7&0\\\hline\phantom{lll}&&&3&\phantom{.}&0&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{0}\\\phantom{lll}&&&2&\phantom{.}&8&0\\\hline\phantom{lll}&&&&&2&0&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{0}\\\phantom{lll}&&&&&1&7&5\\\hline\phantom{lll}&&&&&&2&5&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&4&5\\\hline\phantom{lll}&&&&&&&&5&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\\\hline\phantom{lll}&&&&&&&&1&5&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&0\\\hline\phantom{lll}&&&&&&&&&1&0&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&7&0\\\hline\phantom{lll}&&&&&&&&&&3&0&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&2&8&0\\\hline\phantom{lll}&&&&&&&&&&&2&0&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&1&7&5\\\hline\phantom{lll}&&&&&&&&&&&&\color{DarkBlue}{2}&\color{DarkBlue}{5}&\color{DarkBlue}{0}\\&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&2&4&5\\\hline\phantom{lll}&&&&&&&&&&&&&&5&0\end{array}&\begin{array}{c}\end{array}\end{array}

Step 15

How many 35's are in 50? The answer is 1.

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

Now, 50-1 \cdot 35 = 50 - 35= 15.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccccc}0&0&7&4&.&2&8&5&7&1&4&2&8&5&7&\color{BlueViolet}{1}&\phantom{4}&\phantom{2}\end{array}&\\\color{Magenta}{35}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccccc}2&6&0&0&.&0&0&0&0&0&0&0&0&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllllllllllll}-&\phantom{6}&\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{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&6&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&6&0&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}2&4&5&\phantom{.}\\\hline\phantom{lll}&1&5&0&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}&1&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\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{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7&0\\\hline\phantom{lll}&&&3&\phantom{.}&0&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{0}\\\phantom{lll}&&&2&\phantom{.}&8&0\\\hline\phantom{lll}&&&&&2&0&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{0}\\\phantom{lll}&&&&&1&7&5\\\hline\phantom{lll}&&&&&&2&5&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&4&5\\\hline\phantom{lll}&&&&&&&&5&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\\\hline\phantom{lll}&&&&&&&&1&5&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&0\\\hline\phantom{lll}&&&&&&&&&1&0&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&7&0\\\hline\phantom{lll}&&&&&&&&&&3&0&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&2&8&0\\\hline\phantom{lll}&&&&&&&&&&&2&0&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&1&7&5\\\hline\phantom{lll}&&&&&&&&&&&&2&5&0\\&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&2&4&5\\\hline\phantom{lll}&&&&&&&&&&&&&&\color{BlueViolet}{5}&\color{BlueViolet}{0}\\&&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&&&&&&&1&5&0\end{array}&\begin{array}{c}\end{array}\end{array}

Step 16

How many 35's are in 150? The answer is 4.

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

Now, 150-4 \cdot 35 = 150 - 140= 10.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccccc}0&0&7&4&.&2&8&5&7&1&4&2&8&5&7&1&\color{Crimson}{4}&\phantom{2}\end{array}&\\\color{Magenta}{35}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccccc}2&6&0&0&.&0&0&0&0&0&0&0&0&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllllllllllll}-&\phantom{6}&\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{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&6&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&6&0&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}2&4&5&\phantom{.}\\\hline\phantom{lll}&1&5&0&\phantom{.}\\-&\phantom{6}&\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{0}\\\phantom{lll}&1&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\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{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&7&0\\\hline\phantom{lll}&&&3&\phantom{.}&0&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{0}\\\phantom{lll}&&&2&\phantom{.}&8&0\\\hline\phantom{lll}&&&&&2&0&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{0}\\\phantom{lll}&&&&&1&7&5\\\hline\phantom{lll}&&&&&&2&5&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&4&5\\\hline\phantom{lll}&&&&&&&&5&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\\\hline\phantom{lll}&&&&&&&&1&5&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&0\\\hline\phantom{lll}&&&&&&&&&1&0&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&7&0\\\hline\phantom{lll}&&&&&&&&&&3&0&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&2&8&0\\\hline\phantom{lll}&&&&&&&&&&&2&0&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&1&7&5\\\hline\phantom{lll}&&&&&&&&&&&&2&5&0\\&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&2&4&5\\\hline\phantom{lll}&&&&&&&&&&&&&&5&0\\&&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&&3&5\\\hline\phantom{lll}&&&&&&&&&&&&&&\color{Crimson}{1}&\color{Crimson}{5}&\color{Crimson}{0}\\&&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&&1&4&0\\\hline\phantom{lll}&&&&&&&&&&&&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}

Step 17

How many 35's are in 100? The answer is 2.

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

Now, 100-2 \cdot 35 = 100 - 70= 30.

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As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: \frac{2600}{35}=74.2 \overline{857142}

Answer: \frac{2600}{35}=74.2\overline{857142}