Murtoluvusta desimaaliluvuksi -laskin

Your input: convert $$$\frac{1700}{60}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{2}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\60&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&7&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$60$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-60 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Purple}{0}&\phantom{0}&\phantom{2}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Purple}{1}& 7 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$60$$$'s are in $$$17$$$?

The answer is $$$0$$$.

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

Now, $$$17-60 \cdot 0 = 17 - 0= 17$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{Chartreuse}{0}&\phantom{2}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{1}&\color{Chartreuse}{7}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$60$$$'s are in $$$170$$$?

The answer is $$$2$$$.

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

Now, $$$170-60 \cdot 2 = 170 - 120= 50$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{Crimson}{2}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Crimson}{1}&\color{Crimson}{7}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&5&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$60$$$'s are in $$$500$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$500-60 \cdot 8 = 500 - 480= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&2&\color{DarkCyan}{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&\color{DarkCyan}{5}&\color{DarkCyan}{0}&\color{DarkCyan}{0}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&8&0&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$60$$$'s are in $$$200$$$?

The answer is $$$3$$$.

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

Now, $$$200-60 \cdot 3 = 200 - 180= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&2&8&.&\color{Blue}{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&5&0&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&8&0&\phantom{.}\\\hline\phantom{lll}&&\color{Blue}{2}&\color{Blue}{0}&\phantom{.}&\color{Blue}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&8&\phantom{.}&0\\\hline\phantom{lll}&&&2&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$60$$$'s are in $$$200$$$?

The answer is $$$3$$$.

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

Now, $$$200-60 \cdot 3 = 200 - 180= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&2&8&.&3&\color{Fuchsia}{3}&\phantom{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&5&0&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&8&0&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&8&\phantom{.}&0\\\hline\phantom{lll}&&&\color{Fuchsia}{2}&\phantom{.}&\color{Fuchsia}{0}&\color{Fuchsia}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&8&0\\\hline\phantom{lll}&&&&&2&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$60$$$'s are in $$$200$$$?

The answer is $$$3$$$.

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

Now, $$$200-60 \cdot 3 = 200 - 180= 20$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&2&8&.&3&3&\color{GoldenRod}{3}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&5&0&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&8&0&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&8&\phantom{.}&0\\\hline\phantom{lll}&&&2&\phantom{.}&0&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&8&0\\\hline\phantom{lll}&&&&&\color{GoldenRod}{2}&\color{GoldenRod}{0}&\color{GoldenRod}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&8&0\\\hline\phantom{lll}&&&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1700}{60}=28.3 \overline{3}$$$

Answer: $$$\frac{1700}{60}=28.3\overline{3}$$$