Solution - Base conversion

$${\left(4A5\right)}_{16}$$

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

$$4\cdot {16}^2+10\cdot {16}^1+5\cdot {16}^0$$

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

$$1189$$

Expand each digit by place value: $$4·{16}^2$$
+ $$10·{16}^1$$
+ $$5·{16}^0$$. This gives $$1,189$$ in base 10.

$$1189\left(base10\right)$$

Use repeated division by the target base.

$$\frac{1189}{10}$$

Record quotient and remainder for this division cycle.

$$1189=10\cdot 118+9$$

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.

$$1189$$

Final converted representation in the target base.

$${\left(1189\right)}_{10}$$

Repeatedly divide $$1,189$$ by $$10$$, collect remainders, and read them in reverse to get $$1,189$$.