The correct expanded form of 31,476.52 is:
\[ (3 \times 10,000) + (1 \times 1,000) + (4 \times 100) + (7 \times 10) + (6 \times 1) + (5 \times \frac{1}{10}) + (2 \times \frac{1}{100}) \]
This is equivalent to:
- \(3 \times 10,000\) for the ten-thousands place,
- \(1 \times 1,000\) for the thousands place,
- \(4 \times 100\) for the hundreds place,
- \(7 \times 10\) for the tens place,
- \(6 \times 1\) for the units place,
- \(5 \times \frac{1}{10}\) for the tenths place,
- \(2 \times \frac{1}{100}\) for the hundredths place.
However, let’s review the options provided in your question to find the closest match:
The first option correctly lays out the components of the number but contains an error in interpreting \(5\) and \(2\):
- \(5\) should correspond to \(5 \times \frac{1}{10}\) (for the tenths place),
- \(2\) should correspond to \(2 \times \frac{1}{100}\) (for the hundredths place).
Thus, the closest option to the correct expanded form is:
(3×10,000)+(1×1,000)+(4×100)+(7×10)+(6×1)+(5×(1/10))+(2×(1/100))
If we compare that with the options, the first one is the EASIEST to understand, also flagging to ensure you have to convert decimals appropriately for further calculations as provided.