Fraction to Decimal Calculator

Your input: convert $$$\frac{100}{64}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{1}&\phantom{.}&\phantom{5}&\phantom{6}&\phantom{2}&\phantom{5}\end{array}&\\64&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}1&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$64$$$'s are in $$$1$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$1-64 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Peru}{0}&\phantom{0}&\phantom{1}&\phantom{.}&\phantom{5}&\phantom{6}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{64}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Peru}{1}& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$64$$$'s are in $$$10$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$10-64 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{DeepPink}{0}&\phantom{1}&\phantom{.}&\phantom{5}&\phantom{6}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{64}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{1}&\color{DeepPink}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$64$$$'s are in $$$100$$$?

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$100-64 \cdot 1 = 100 - 64= 36$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{Chartreuse}{1}&\phantom{.}&\phantom{5}&\phantom{6}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{64}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{1}&\color{Chartreuse}{0}&\color{Chartreuse}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&6&4&\phantom{.}\\\hline\phantom{lll}&3&6&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$64$$$'s are in $$$360$$$?

The answer is $$$5$$$.

Write down $$$5$$$ in the upper part of the table.

Now, $$$360-64 \cdot 5 = 360 - 320= 40$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&1&.&\color{GoldenRod}{5}&\phantom{6}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{64}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&6&4&\phantom{.}\\\hline\phantom{lll}&\color{GoldenRod}{3}&\color{GoldenRod}{6}&\phantom{.}&\color{GoldenRod}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&2&\phantom{.}&0\\\hline\phantom{lll}&&4&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$64$$$'s are in $$$400$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$400-64 \cdot 6 = 400 - 384= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&1&.&5&\color{Red}{6}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{64}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&6&4&\phantom{.}\\\hline\phantom{lll}&3&6&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&2&\phantom{.}&0\\\hline\phantom{lll}&&\color{Red}{4}&\phantom{.}&\color{Red}{0}&\color{Red}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&8&4\\\hline\phantom{lll}&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$64$$$'s are in $$$160$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$160-64 \cdot 2 = 160 - 128= 32$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&1&.&5&6&\color{OrangeRed}{2}&\phantom{5}\end{array}&\\\color{Magenta}{64}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&6&4&\phantom{.}\\\hline\phantom{lll}&3&6&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&2&\phantom{.}&0\\\hline\phantom{lll}&&4&\phantom{.}&0&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&8&4\\\hline\phantom{lll}&&&&\color{OrangeRed}{1}&\color{OrangeRed}{6}&\color{OrangeRed}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&2&8\\\hline\phantom{lll}&&&&&3&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$64$$$'s are in $$$320$$$?

The answer is $$$5$$$.

Write down $$$5$$$ in the upper part of the table.

Now, $$$320-64 \cdot 5 = 320 - 320= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&1&.&5&6&2&\color{DarkBlue}{5}\end{array}&\\\color{Magenta}{64}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&6&4&\phantom{.}\\\hline\phantom{lll}&3&6&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&2&\phantom{.}&0\\\hline\phantom{lll}&&4&\phantom{.}&0&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&8&4\\\hline\phantom{lll}&&&&1&6&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&2&8\\\hline\phantom{lll}&&&&&\color{DarkBlue}{3}&\color{DarkBlue}{2}&\color{DarkBlue}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&2&0\\\hline\phantom{lll}&&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Since the remainder is $$$0$$$, then we are done.

Therefore, $$$\frac{100}{64}=1.5625$$$

Answer: $$$\frac{100}{64}=1.5625$$$