Loading [MathJax]/jax/output/HTML-CSS/fonts/TeX/fontdata.js

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 11002 into a decimal.

Write the problem in the special format:

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{5}&\phantom{5}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\2&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&1&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 1

How many 2's are in 1? The answer is 0.

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

Now, 1-0 \cdot 2 = 1 - 0= 1.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{DeepPink}{0}&\phantom{5}&\phantom{5}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{2}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{DeepPink}{1}& 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}1&1&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 2

How many 2's are in 11? The answer is 5.

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

Now, 11-5 \cdot 2 = 11 - 10= 1.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{OrangeRed}{5}&\phantom{5}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{2}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&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{OrangeRed}{1}&\color{OrangeRed}{1}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 3

How many 2's are in 10? The answer is 5.

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

Now, 10-5 \cdot 2 = 10 - 10= 0.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&5&\color{Crimson}{5}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{2}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&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}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&\phantom{.}\\\hline\phantom{lll}&\color{Crimson}{1}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 4

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

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

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

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&5&5&\color{BlueViolet}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{2}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&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}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&0&\phantom{.}\\\hline\phantom{lll}&&\color{BlueViolet}{0}&\color{BlueViolet}{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 2's are in 0? The answer is 0.

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

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

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&5&5&0&.&\color{Red}{0}\end{array}&\\\color{Magenta}{2}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&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}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Red}{0}&\phantom{.}&\color{Red}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}

Since the remainder is 0, then we are done.

Therefore, \frac{1100}{2}=550.0

Answer: \frac{1100}{2}=550.0