2. Construct Arguments Kim writes an estimate for the number 0.00436 as \( 4 \times 10^{3} \), Explain why this cannot be correct.

To evaluate Kim's estimate of the number 0.00436 as \( 4 \times 10^{3} \), we need to analyze the expression and the value it represents. 1. **Understanding Scientific Notation**: The expression \( 4 \times 10^{3} \) is in scientific notation, where the number is represented as a coefficient (4) multiplied by a power of ten (10 raised to the power of 3). 2. **Calculating the Value**: When we calculate \( 4 \times 10^{3} \), we get: \[ 4 \times 10^{3} = 4 \times 1000 = 4000 \] 3. **Comparing Values**: Now, we compare this result (4000) with the original number (0.00436): - 0.00436 is a very small number, much less than 1. - 4000 is a large number, significantly greater than 1. 4. **Conclusion**: Since 0.00436 and 4000 are vastly different in magnitude (one is a small decimal and the other is a large whole number), Kim's estimate cannot be correct. The correct scientific notation for 0.00436 would be \( 4.36 \times 10^{-3} \), which accurately represents the small value of 0.00436. In summary, Kim's estimate of \( 4 \times 10^{3} \) is incorrect because it represents a value (4000) that is not even close to the original number (0.00436).