Solution - Base conversion

$${\left(\forall A\right)}_{16}$$

Expand digits with place-value powers in the source base.

$$10\cdot {16}^2+10\cdot {16}^1+10\cdot {16}^0$$

Sum the expanded terms to obtain the base-10 value.

$$2730$$

Expand each digit by place value: $$10·{16}^2$$
+ $$10·{16}^1$$
+ $$10·{16}^0$$. This gives $$2,730$$ in base 10.

$$2730\left(base10\right)$$

Use repeated division by the target base.

$$\frac{2730}{10}$$

Record quotient and remainder for this division cycle.

$$2730=10\cdot 273+0$$

Record quotient and remainder for this division cycle.

$$273=10\cdot 27+3$$

Record quotient and remainder for this division cycle.

$$27=10\cdot 2+7$$

Record quotient and remainder for this division cycle.

$$2=10\cdot 0+2$$

Read remainders from last to first to form target-base digits.

$$2730$$

Final converted representation in the target base.

$${\left(2730\right)}_{10}$$

Repeatedly divide $$2,730$$ by $$10$$, collect remainders, and read them in reverse to get $$2,730$$.