Long Division Calculator
Perform the long division of numbers step by step
The calculator will divide any two numbers (positive or negative, integer or decimal), with steps shown. Enter the dividend and the divisor and get the quotient to the given precision without remainder or quotient with remainder.
Related calculator: Polynomial Long Division Calculator
Solution
Your input: find 408.0160.0 using long division.
Move the decimal point 1 place to the right in both numbers. It is equivalent to multiplying the numbers by 101=10:
408.0⋅10=4080 and 160.0⋅10=1600.
Write the problem in the special format:
\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{0}&\phantom{0}&\phantom{0}&\phantom{2}\end{array}&\\1600&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}4&0&8&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}
Step 1
How many 1600's are in 4? The answer is 0.
Write down the calculated result in the upper part of the table.
Now, 4-0 \cdot 1600 = 4 - 0= 4.
Bring down the next digit of the dividend.
\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\color{Violet}{0}&\phantom{0}&\phantom{0}&\phantom{2}\end{array}&\\\color{Magenta}{1600}&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}\color{Violet}{4}& 0 \downarrow&8&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}0\\\hline\phantom{lll}4&0\end{array}&\begin{array}{c}\end{array}\end{array}
Step 2
How many 1600's are in 40? The answer is 0.
Write down the calculated result in the upper part of the table.
Now, 40-0 \cdot 1600 = 40 - 0= 40.
Bring down the next digit of the dividend.
\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}0&\color{Blue}{0}&\phantom{0}&\phantom{2}\end{array}&\\\color{Magenta}{1600}&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}4&0& 8 \downarrow&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}0\\\hline\phantom{lll}\color{Blue}{4}&\color{Blue}{0}\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}&0\\\hline\phantom{lll}4&0&8\end{array}&\begin{array}{c}\end{array}\end{array}
Step 3
How many 1600's are in 408? The answer is 0.
Write down the calculated result in the upper part of the table.
Now, 408-0 \cdot 1600 = 408 - 0= 408.
Bring down the next digit of the dividend.
\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}0&0&\color{Peru}{0}&\phantom{2}\end{array}&\\\color{Magenta}{1600}&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}4&0&8& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}0\\\hline\phantom{lll}4&0\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}&0\\\hline\phantom{lll}\color{Peru}{4}&\color{Peru}{0}&\color{Peru}{8}\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}&&0\\\hline\phantom{lll}4&0&8&0\end{array}&\begin{array}{c}\end{array}\end{array}
Step 4
How many 1600's are in 4080? The answer is 2.
Write down the calculated result in the upper part of the table.
Now, 4080-2 \cdot 1600 = 4080 - 3200= 880.
\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}0&0&0&\color{Brown}{2}\end{array}&\\\color{Magenta}{1600}&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}4&0&8&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}0\\\hline\phantom{lll}4&0\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}&0\\\hline\phantom{lll}4&0&8\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}&&0\\\hline\phantom{lll}\color{Brown}{4}&\color{Brown}{0}&\color{Brown}{8}&\color{Brown}{0}\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}3&2&0&0\\\hline\phantom{lll}&8&8&0\end{array}&\begin{array}{c}\end{array}\end{array}
Since the remainder is greater than the divisor, then we are done.
Therefore, \frac{4080}{1600}=2+\frac{880}{1600}=2+\frac{11}{20}
Answer: \frac{408.0}{160.0}=2+\frac{11}{20}