Question

What is the expanded form of 23.75?

A. (5*10)+(7*1)+(3*1/10)+(2*1/100)
B. (2*10)+(3*1)+(7*1/10)+(5*1/100)
C. (2*10)+(3*1)+(5*1/10)+(7*1/100)
D. (2*10)+(3*1)+(7*1/1^10)+(5*1/2^10)

Answer 1

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**: \((2 \times 10) + (3 \times 1) + (7 \times \frac{1}{10}) + (5 \times \frac{1}{100})\).