The problem provided involves analyzing and correcting an expanded form of the number 604.29.

The Student's Expression:

$(6 \times 100) + (4 \times 10) + (2 \times 1) + \left(9 \times \frac{1}{10}\right)$

Correct Analysis:

The student's expression correctly represents the integer part of 604.29, but it fails to fully represent the decimal part accurately. Here's why:

1. Integer Part (Correct):

   • $6 \times 100 = 600$
   • $4 \times 10 = 40$
   • $2 \times 1 = 2$

   The sum of these values is $600 + 40 + 2 = 642$, which is not correct because the expression sums up to a number larger than 604.29, and it misses a key part.

2. Decimal Part (Incorrect):

   • $9 \times \frac{1}{10}$ does represent 0.9 but does not account for the other decimal place.
   • The correct representation of the decimal part (0.29) should include both the tenths and hundredths place.

Correct Expanded Form:

To accurately express 604.29 in expanded form: $(6 \times 100) + (0 \times 10) + (4 \times 1) + \left(2 \times \frac{1}{10}\right) + \left(9 \times \frac{1}{100}\right)$

Steps to Correct:

• The first term remains $6 \times 100$.
• The tens place should be $0 \times 10$.
• The units place should be $4 \times 1$.
• The tenths place should be $2 \times \frac{1}{10}$, which equals 0.2.
• The hundredths place should be $9 \times \frac{1}{100}$, which equals 0.09.

Thus, the correct expanded form is: $(6 \times 100) + (0 \times 10) + (4 \times 1) + \left(2 \times \frac{1}{10}\right) + \left(9 \times \frac{1}{100}\right)$

This form correctly represents the number 604.29.

Would you like more details on this correction or have any questions?

Here are five related questions:

1. How do you expand a number like 732.56 in expanded form?
2. What is the significance of each place value in the decimal system?
3. How would you express 0.045 in expanded form?
4. How can errors in expanded form impact mathematical calculations?
5. What is the correct expanded form of 102.309?

Tip: When writing numbers in expanded form, remember to include all place values, even if the coefficient is zero.