Evaluate
\frac{500}{327}\approx 1.529051988
Factor
\frac{2 ^ {2} \cdot 5 ^ {3}}{3 \cdot 109} = 1\frac{173}{327} = 1.529051987767584
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\begin{array}{l}\phantom{327000000)}\phantom{1}\\327000000\overline{)500000000}\\\end{array}
Use the 1^{st} digit 5 from dividend 500000000
\begin{array}{l}\phantom{327000000)}0\phantom{2}\\327000000\overline{)500000000}\\\end{array}
Since 5 is less than 327000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{327000000)}0\phantom{3}\\327000000\overline{)500000000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 500000000
\begin{array}{l}\phantom{327000000)}00\phantom{4}\\327000000\overline{)500000000}\\\end{array}
Since 50 is less than 327000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{327000000)}00\phantom{5}\\327000000\overline{)500000000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 500000000
\begin{array}{l}\phantom{327000000)}000\phantom{6}\\327000000\overline{)500000000}\\\end{array}
Since 500 is less than 327000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{327000000)}000\phantom{7}\\327000000\overline{)500000000}\\\end{array}
Use the 4^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{327000000)}0000\phantom{8}\\327000000\overline{)500000000}\\\end{array}
Since 5000 is less than 327000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{327000000)}0000\phantom{9}\\327000000\overline{)500000000}\\\end{array}
Use the 5^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{327000000)}00000\phantom{10}\\327000000\overline{)500000000}\\\end{array}
Since 50000 is less than 327000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{327000000)}00000\phantom{11}\\327000000\overline{)500000000}\\\end{array}
Use the 6^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{327000000)}000000\phantom{12}\\327000000\overline{)500000000}\\\end{array}
Since 500000 is less than 327000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{327000000)}000000\phantom{13}\\327000000\overline{)500000000}\\\end{array}
Use the 7^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{327000000)}0000000\phantom{14}\\327000000\overline{)500000000}\\\end{array}
Since 5000000 is less than 327000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{327000000)}0000000\phantom{15}\\327000000\overline{)500000000}\\\end{array}
Use the 8^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{327000000)}00000000\phantom{16}\\327000000\overline{)500000000}\\\end{array}
Since 50000000 is less than 327000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{327000000)}00000000\phantom{17}\\327000000\overline{)500000000}\\\end{array}
Use the 9^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{327000000)}000000001\phantom{18}\\327000000\overline{)500000000}\\\phantom{327000000)}\underline{\phantom{}327000000\phantom{}}\\\phantom{327000000)}173000000\\\end{array}
Find closest multiple of 327000000 to 500000000. We see that 1 \times 327000000 = 327000000 is the nearest. Now subtract 327000000 from 500000000 to get reminder 173000000. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }173000000
Since 173000000 is less than 327000000, stop the division. The reminder is 173000000. The topmost line 000000001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}