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\begin{array}{l}\phantom{10)}\phantom{1}\\10\overline{)90}\\\end{array}
Use the 1^{st} digit 9 from dividend 90
\begin{array}{l}\phantom{10)}0\phantom{2}\\10\overline{)90}\\\end{array}
Since 9 is less than 10, use the next digit 0 from dividend 90 and add 0 to the quotient
\begin{array}{l}\phantom{10)}0\phantom{3}\\10\overline{)90}\\\end{array}
Use the 2^{nd} digit 0 from dividend 90
\begin{array}{l}\phantom{10)}09\phantom{4}\\10\overline{)90}\\\phantom{10)}\underline{\phantom{}90\phantom{}}\\\phantom{10)99}0\\\end{array}
Find closest multiple of 10 to 90. We see that 9 \times 10 = 90 is the nearest. Now subtract 90 from 90 to get reminder 0. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }0
Since 0 is less than 10, stop the division. The reminder is 0. The topmost line 09 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.