1. **Write the number 3334 in expanded form using exponents.** The number 3334 can be broken down by place value: $$3334 = 3 \times 10^3 + 3 \times 10^2 + 3 \times 10^1 + 4 \times 10^0$$ 2. **Add 31.25 + 23.47.** Align the decimal points and add: $$\begin{array}{r} 31.25 \\ + 23.47 \\ \hline 54.72 \end{array}$$ So, the sum is $54.72$. 3. **Write the number nine million five hundred sixty-one thousand six hundred five in standard form.** This number is: $$9,561,605$$ 4. **Multiply 236.7 by 0.34.** Step 1: Multiply as if no decimals: $$2367 \times 34 = ?$$ Calculate: $$2367 \times 34 = 2367 \times (30 + 4) = 2367 \times 30 + 2367 \times 4 = 71010 + 9468 = 80478$$ Step 2: Count decimal places: 236.7 has 1 decimal place, 0.34 has 2 decimal places, total 3 decimal places. Step 3: Place decimal point 3 places from right: $$80.478$$ So, the product is $80.478$. 5. **Order the fractions $\frac{1}{2}$, $\frac{3}{9}$, $\frac{5}{14}$ from greatest to least.** Convert to decimals: $$\frac{1}{2} = 0.5$$ $$\frac{3}{9} = \frac{1}{3} \approx 0.333$$ $$\frac{5}{14} \approx 0.357$$ Order: $$0.5 > 0.357 > 0.333$$ So, from greatest to least: $$\frac{1}{2}, \frac{5}{14}, \frac{3}{9}$$