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Calculadora de frações para decimais

Converter frações em decimais, passo a passo

A calculadora converterá a fração dada (própria ou imprópria) ou o número misto em um decimal (possivelmente, repetitivo ou recorrente), com as etapas mostradas.

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 210030 into a decimal.

Write the problem in the special format:

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{7}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\30&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}2&1&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 1

How many 30's are in 2? The answer is 0.

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

Now, 2-0 \cdot 30 = 2 - 0= 2.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Blue}{0}&\phantom{0}&\phantom{7}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Blue}{2}& 1 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&1&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 2

How many 30's are in 21? The answer is 0.

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

Now, 21-0 \cdot 30 = 21 - 0= 21.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Peru}{0}&\phantom{7}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&1& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{2}&\color{Peru}{1}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 3

How many 30's are in 210? The answer is 7.

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

Now, 210-7 \cdot 30 = 210 - 210= 0.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Red}{7}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&1&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Red}{2}&\color{Red}{1}&\color{Red}{0}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&1&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 4

How many 30's are in 0? The answer is 0.

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

Now, 0-0 \cdot 30 = 0 - 0= 0.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&7&\color{DeepPink}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&1&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&1&0&\phantom{.}\\\hline\phantom{lll}&&\color{DeepPink}{0}&\color{DeepPink}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}

Step 5

How many 30's are in 0? The answer is 0.

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

Now, 0-0 \cdot 30 = 0 - 0= 0.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&7&0&.&\color{Green}{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&1&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&1&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Green}{0}&\phantom{.}&\color{Green}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: \frac{2100}{30}=70. \overline{0}

Answer: \frac{2100}{30}=70.\overline{0}