Evaluate
\frac{1000000}{9}\approx 111111.111111111
Factor
\frac{2 ^ {6} \cdot 5 ^ {6}}{3 ^ {2}} = 111111\frac{1}{9} = 111111.11111111111
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)3000000}\\\end{array}
Use the 1^{st} digit 3 from dividend 3000000
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)3000000}\\\end{array}
Since 3 is less than 27, use the next digit 0 from dividend 3000000 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)3000000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 3000000
\begin{array}{l}\phantom{27)}01\phantom{4}\\27\overline{)3000000}\\\phantom{27)}\underline{\phantom{}27\phantom{99999}}\\\phantom{27)9}3\\\end{array}
Find closest multiple of 27 to 30. We see that 1 \times 27 = 27 is the nearest. Now subtract 27 from 30 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{27)}01\phantom{5}\\27\overline{)3000000}\\\phantom{27)}\underline{\phantom{}27\phantom{99999}}\\\phantom{27)9}30\\\end{array}
Use the 3^{rd} digit 0 from dividend 3000000
\begin{array}{l}\phantom{27)}011\phantom{6}\\27\overline{)3000000}\\\phantom{27)}\underline{\phantom{}27\phantom{99999}}\\\phantom{27)9}30\\\phantom{27)}\underline{\phantom{9}27\phantom{9999}}\\\phantom{27)99}3\\\end{array}
Find closest multiple of 27 to 30. We see that 1 \times 27 = 27 is the nearest. Now subtract 27 from 30 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{27)}011\phantom{7}\\27\overline{)3000000}\\\phantom{27)}\underline{\phantom{}27\phantom{99999}}\\\phantom{27)9}30\\\phantom{27)}\underline{\phantom{9}27\phantom{9999}}\\\phantom{27)99}30\\\end{array}
Use the 4^{th} digit 0 from dividend 3000000
\begin{array}{l}\phantom{27)}0111\phantom{8}\\27\overline{)3000000}\\\phantom{27)}\underline{\phantom{}27\phantom{99999}}\\\phantom{27)9}30\\\phantom{27)}\underline{\phantom{9}27\phantom{9999}}\\\phantom{27)99}30\\\phantom{27)}\underline{\phantom{99}27\phantom{999}}\\\phantom{27)999}3\\\end{array}
Find closest multiple of 27 to 30. We see that 1 \times 27 = 27 is the nearest. Now subtract 27 from 30 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{27)}0111\phantom{9}\\27\overline{)3000000}\\\phantom{27)}\underline{\phantom{}27\phantom{99999}}\\\phantom{27)9}30\\\phantom{27)}\underline{\phantom{9}27\phantom{9999}}\\\phantom{27)99}30\\\phantom{27)}\underline{\phantom{99}27\phantom{999}}\\\phantom{27)999}30\\\end{array}
Use the 5^{th} digit 0 from dividend 3000000
\begin{array}{l}\phantom{27)}01111\phantom{10}\\27\overline{)3000000}\\\phantom{27)}\underline{\phantom{}27\phantom{99999}}\\\phantom{27)9}30\\\phantom{27)}\underline{\phantom{9}27\phantom{9999}}\\\phantom{27)99}30\\\phantom{27)}\underline{\phantom{99}27\phantom{999}}\\\phantom{27)999}30\\\phantom{27)}\underline{\phantom{999}27\phantom{99}}\\\phantom{27)9999}3\\\end{array}
Find closest multiple of 27 to 30. We see that 1 \times 27 = 27 is the nearest. Now subtract 27 from 30 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{27)}01111\phantom{11}\\27\overline{)3000000}\\\phantom{27)}\underline{\phantom{}27\phantom{99999}}\\\phantom{27)9}30\\\phantom{27)}\underline{\phantom{9}27\phantom{9999}}\\\phantom{27)99}30\\\phantom{27)}\underline{\phantom{99}27\phantom{999}}\\\phantom{27)999}30\\\phantom{27)}\underline{\phantom{999}27\phantom{99}}\\\phantom{27)9999}30\\\end{array}
Use the 6^{th} digit 0 from dividend 3000000
\begin{array}{l}\phantom{27)}011111\phantom{12}\\27\overline{)3000000}\\\phantom{27)}\underline{\phantom{}27\phantom{99999}}\\\phantom{27)9}30\\\phantom{27)}\underline{\phantom{9}27\phantom{9999}}\\\phantom{27)99}30\\\phantom{27)}\underline{\phantom{99}27\phantom{999}}\\\phantom{27)999}30\\\phantom{27)}\underline{\phantom{999}27\phantom{99}}\\\phantom{27)9999}30\\\phantom{27)}\underline{\phantom{9999}27\phantom{9}}\\\phantom{27)99999}3\\\end{array}
Find closest multiple of 27 to 30. We see that 1 \times 27 = 27 is the nearest. Now subtract 27 from 30 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{27)}011111\phantom{13}\\27\overline{)3000000}\\\phantom{27)}\underline{\phantom{}27\phantom{99999}}\\\phantom{27)9}30\\\phantom{27)}\underline{\phantom{9}27\phantom{9999}}\\\phantom{27)99}30\\\phantom{27)}\underline{\phantom{99}27\phantom{999}}\\\phantom{27)999}30\\\phantom{27)}\underline{\phantom{999}27\phantom{99}}\\\phantom{27)9999}30\\\phantom{27)}\underline{\phantom{9999}27\phantom{9}}\\\phantom{27)99999}30\\\end{array}
Use the 7^{th} digit 0 from dividend 3000000
\begin{array}{l}\phantom{27)}0111111\phantom{14}\\27\overline{)3000000}\\\phantom{27)}\underline{\phantom{}27\phantom{99999}}\\\phantom{27)9}30\\\phantom{27)}\underline{\phantom{9}27\phantom{9999}}\\\phantom{27)99}30\\\phantom{27)}\underline{\phantom{99}27\phantom{999}}\\\phantom{27)999}30\\\phantom{27)}\underline{\phantom{999}27\phantom{99}}\\\phantom{27)9999}30\\\phantom{27)}\underline{\phantom{9999}27\phantom{9}}\\\phantom{27)99999}30\\\phantom{27)}\underline{\phantom{99999}27\phantom{}}\\\phantom{27)999999}3\\\end{array}
Find closest multiple of 27 to 30. We see that 1 \times 27 = 27 is the nearest. Now subtract 27 from 30 to get reminder 3. Add 1 to quotient.
\text{Quotient: }111111 \text{Reminder: }3
Since 3 is less than 27, stop the division. The reminder is 3. The topmost line 0111111 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 111111.
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}