Question

Math 8 Q1 (Pre-Algebra) / The Number System
What is the expanded form of 23.75?(1 point)
Responses

(2×10)+(3×1)+(7×1101)+(5×1102)
(2×10)+(3×1)+(7×110)+(5×1100)
(2×10)+(3×1)+(5×110)+(7×1100)
(5×10)+(7×1)+(3×110)+(2×1100)

Answer 1

To express the number 23.75 in expanded form, we can break it down according to the place values of each digit.

- The digit '2' is in the tens place, so it represents \(2 \times 10\).
- The digit '3' is in the ones place, so it represents \(3 \times 1\).
- The digit '7' is in the tenths place (0.7), so it represents \(7 \times 0.1\) (which is also equivalent to \(7 \times 10^{-1}\)).
- The digit '5' is in the hundredths place (0.05), so it represents \(5 \times 0.01\) (which is also equivalent to \(5 \times 10^{-2}\)).

Combining these values, we have:

\[
(2 \times 10) + (3 \times 1) + (7 \times 10^{-1}) + (5 \times 10^{-2})
\]

Now, looking at the answer choices, the second option is:

\((2 \times 10) + (3 \times 1) + (7 \times 10^{1}) + (5 \times 10^{0})\)

This is incorrect because it inaccurately represents the decimal place values.

The correct expression in expanded form from the given options is:

\((2 \times 10) + (3 \times 1) + (7 \times 10^{-1}) + (5 \times 10^{-2})\)

Since none of the listed options clearly match the correct expanded form, please check the answer choices carefully to ensure there is no mistake. If there appears to be a mismatch, it is possible that the options are misstated.

Without error in the answer choices, and based on the expanded multiplication, the correct representation should be:

\((2 \times 10) + (3 \times 1) + (7 \times 10^{-1}) + (5 \times 10^{-2})\)