Υπολογιστής μετατροπής κλάσματος σε δεκαδικό

Your input: convert $$$\frac{1500}{16}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{9}&\phantom{3}&\phantom{.}&\phantom{7}&\phantom{5}\end{array}&\\16&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&5&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$16$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-16 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Blue}{0}&\phantom{0}&\phantom{9}&\phantom{3}&\phantom{.}&\phantom{7}&\phantom{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Blue}{1}& 5 \downarrow&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$16$$$'s are in $$$15$$$?

The answer is $$$0$$$.

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

Now, $$$15-16 \cdot 0 = 15 - 0= 15$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Green}{0}&\phantom{9}&\phantom{3}&\phantom{.}&\phantom{7}&\phantom{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&5& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Green}{1}&\color{Green}{5}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$16$$$'s are in $$$150$$$?

The answer is $$$9$$$.

Write down $$$9$$$ in the upper part of the table.

Now, $$$150-16 \cdot 9 = 150 - 144= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{Purple}{9}&\phantom{3}&\phantom{.}&\phantom{7}&\phantom{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&5&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{5}&\color{Purple}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$16$$$'s are in $$$60$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$60-16 \cdot 3 = 60 - 48= 12$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&9&\color{Brown}{3}&\phantom{.}&\phantom{7}&\phantom{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&5&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&\color{Brown}{6}&\color{Brown}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&8&\phantom{.}\\\hline\phantom{lll}&&1&2&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$16$$$'s are in $$$120$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$120-16 \cdot 7 = 120 - 112= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&9&3&.&\color{DarkMagenta}{7}&\phantom{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&5&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&8&\phantom{.}\\\hline\phantom{lll}&&\color{DarkMagenta}{1}&\color{DarkMagenta}{2}&\phantom{.}&\color{DarkMagenta}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&1&\phantom{.}&2\\\hline\phantom{lll}&&&&&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$16$$$'s are in $$$80$$$?

The answer is $$$5$$$.

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

Now, $$$80-16 \cdot 5 = 80 - 80= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&9&3&.&7&\color{Chocolate}{5}\end{array}&\\\color{Magenta}{16}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&5&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&8&\phantom{.}\\\hline\phantom{lll}&&1&2&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&1&\phantom{.}&2\\\hline\phantom{lll}&&&&&\color{Chocolate}{8}&\color{Chocolate}{0}\\&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&8&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{1500}{16}=93.75$$$

Answer: $$$\frac{1500}{16}=93.75$$$