1. **State the problem:** Calculate $3.7 \times 16.2^2 - 500$ and express the answer in different forms. 2. **Calculate the square:** First, find $16.2^2$. $$16.2^2 = 16.2 \times 16.2 = 262.44$$ 3. **Multiply by 3.7:** $$3.7 \times 262.44 = 970.028$$ 4. **Subtract 500:** $$970.028 - 500 = 470.028$$ 5. **(a) Correct to two decimal places:** Round $470.028$ to two decimal places: $$470.03$$ 6. **(b)(i) Correct to three significant figures:** The first three significant figures of $470.028$ are $470$ (since the zero is significant here): $$470$$ 7. **(b)(ii) Express in the form $a \times 10^k$ where $1 \leq a < 10$ and $k \in \mathbb{Z}$:** Rewrite $470$ as: $$4.70 \times 10^2$$ **Final answers:** (a) $470.03$ (b)(i) $470$ (b)(ii) $4.70 \times 10^2$