To write 23.75 in expanded form, we can break it down based on place value:
- The '2' is in the tens place, representing \(2 \times 10\).
- The '3' is in the ones place, representing \(3 \times 1\).
- The '7' is in the tenths place, representing \(7 \times \frac{1}{10}\) or \(7 \times 10^{-1}\).
- The '5' is in the hundredths place, representing \(5 \times \frac{1}{100}\) or \(5 \times 10^{-2}\).
Putting this all together, the expanded form of 23.75 can be expressed as:
\[ (2 \times 10) + (3 \times 1) + (7 \times \frac{1}{10}) + (5 \times \frac{1}{100}) \]
Now let's review the answer choices:
A. \((2 \times 10)+(3 \times 1)+(7 \times 1/10)+(5 \times 1/100)\)
B. \((5 \times 10)+(7 \times 1)+(3 \times 1/10)+(2 \times 1/100)\)
C. \((2 \times 10)+(3 \times 1)+(5 \times 1/10)+(7 \times 1/100)\)
D. \((2 \times 10)+(3 \times 1)+(7 \times 1/10 \text{ to the first power})+(5 \times 1/10 \text{ to the second power})\)
The correct answer is: A. \((2 \times 10)+(3 \times 1)+(7 \times 1/10)+(5 \times 1/100)\)
This matches the standard expanded form representation.