Solution - Base conversion

$${\left(4A2\right)}_{16}$$

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

$$4\cdot {16}^2+10\cdot {16}^1+2\cdot {16}^0$$

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

$$1186$$

Expand each digit by place value: $$4·{16}^2$$
+ $$10·{16}^1$$
+ $$2·{16}^0$$. This gives $$1,186$$ in base 10.

$$1186\left(base10\right)$$

Use repeated division by the target base.

$$\frac{1186}{10}$$

Record quotient and remainder for this division cycle.

$$1186=10\cdot 118+6$$

Record quotient and remainder for this division cycle.

$$118=10\cdot 11+8$$

Record quotient and remainder for this division cycle.

$$11=10\cdot 1+1$$

Record quotient and remainder for this division cycle.

$$1=10\cdot 0+1$$

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

$$1186$$

Final converted representation in the target base.

$${\left(1186\right)}_{10}$$

Repeatedly divide $$1,186$$ by $$10$$, collect remainders, and read them in reverse to get $$1,186$$.