To find the expanded form of 23.75, we'll break down the number into its place values:
- The "2" in the tens place represents 20 (which is \(2 \times 10\)).
- The "3" in the ones place represents 3 (which is \(3 \times 1\)).
- The "7" in the tenths place represents 0.7 (which is \(7 \times \frac{1}{10}\)).
- The "5" in the hundredths place represents 0.05 (which is \(5 \times \frac{1}{100}\)).
Therefore, the expanded form of 23.75 is:
\[ (2 \times 10) + (3 \times 1) + (7 \times \frac{1}{10}) + (5 \times \frac{1}{100}) \]
Now, let's look at the choices provided:
A. \((5 \times 10) + (7 \times 1) + (3 \times \frac{1}{10}) + (2 \times \frac{1}{100})\) (not correct)
B. \((2 \times 10) + (3 \times 1) + (7 \times \frac{1}{10}) + (5 \times \frac{1}{100})\) (this is correct)
C. \((2 \times 10) + (3 \times 1) + (5 \times \frac{1}{10}) + (7 \times \frac{1}{100})\) (not correct)
D. \((2 \times 10) + (3 \times 1) + (7 \times \frac{1}{1^{10}}) + (5 \times \frac{1}{2^{10}})\) (not correct)
So the correct answer is B: \((2 \times 10) + (3 \times 1) + (7 \times \frac{1}{10}) + (5 \times \frac{1}{100})\).