1. **State the problem:** Find the secret three-digit number based on the clues given. 2. **List the clues:** - The number is below 750. - The ones digit divides evenly into the hundreds and tens digits. - The number is even. - The sum of the ones digit and the tens digit equals the hundreds digit. - All digits are different. 3. **Define digits:** Let the number be $\overline{HTO}$ where $H$ is hundreds, $T$ is tens, and $O$ is ones. 4. **Analyze the clues:** - Since the number is even, $O$ must be even: possible digits are 0, 2, 4, 6, 8. - $O$ divides $H$ and $T$ evenly, so $H \bmod O = 0$ and $T \bmod O = 0$. - $H = T + O$. - $H < 7.5$ (since number < 750, $H$ can be 1 to 7). - All digits distinct. 5. **Try possible $O$ values:** - $O=2$: - $H$ and $T$ divisible by 2. - $H = T + 2$. - $H$ and $T$ even digits. - Possible $H$: 2,4,6. - For $H=4$, $T=2$ (since $4=2+2$), digits 4,2,2 not distinct. - For $H=6$, $T=4$ (since $6=4+2$), digits 6,4,2 distinct. - Check divisibility: 6 mod 2=0, 4 mod 2=0, good. - Number: 642. - $O=4$: - $H$ and $T$ divisible by 4. - $H = T + 4$. - $H$ max 7, so $T$ max 3. - $T$ divisible by 4 means $T=0$ or 4 (4 too big), so $T=0$. - Then $H=0+4=4$. - Digits: 4,0,4 repeated 4, not distinct. - $O=6$: - $H$ and $T$ divisible by 6. - $H = T + 6$. - $H$ max 7, so $T$ max 1. - $T$ divisible by 6 means $T=0$. - Then $H=0+6=6$. - Digits: 6,0,6 repeated 6, not distinct. - $O=8$: - $H$ and $T$ divisible by 8. - $H = T + 8$. - $H$ max 7, impossible. - $O=0$ invalid as division by zero. 6. **Conclusion:** The only number satisfying all conditions is $\boxed{642}$. 7. **Second problem:** Round 0.2982 to nearest hundredth. - Hundredth place is second digit after decimal. - Look at thousandth place (third digit) to decide rounding. - Number: 0.2982 - Hundredth digit: 9 - Thousandth digit: 8 (>=5, so round up) - Rounding 0.2982 to hundredth: $$0.29 \to 0.30$$ **Final answers:** - Secret number: 642 - Rounded number: 0.30