1. **State the problem:** Katrina claims that $3.5 \times 10^4$ is greater than $2.1 \times 10^6$ because $3.5 > 2.1$. 2. **Explain the mistake:** When comparing numbers in scientific notation, you must consider both the coefficient and the power of ten. The power of ten determines the place value, which greatly affects the size of the number. 3. **Convert to standard form:** - $3.5 \times 10^4 = 3.5 \times 10000 = 35000$ - $2.1 \times 10^6 = 2.1 \times 1000000 = 2100000$ 4. **Compare the numbers:** - $35000$ is much smaller than $2100000$ 5. **Conclusion:** - Therefore, $3.5 \times 10^4 < 2.1 \times 10^6$ Katrina's mistake was ignoring the powers of ten, which represent the scale of the numbers. The coefficient alone is not enough to compare numbers in scientific notation.