What is the expanded form of 23.75?

A.(2 x 10)+(3 x 1)+(7 x 1/10)+(5 x 1/100)
B.(5 x 10)+(7 x 1)+(3 x 1/10)+(2 x 1/100)
C.(2 x 10)+(3 x 1)+(5 x 1/10)+(7 x 1/100)
D.(2 x 10)+(3 x 1)+(7 x 1/10 to the first power)+(5 x 1/10 to the secconed power)

1 answer

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.