Question
What power of 10 would make the following equation true?
3.75×10?=0.0000375
(1 point)
Responses
7
7
5
5
-7
-7
-6
-6
6
6
-5
-5
3.75×10?=0.0000375
(1 point)
Responses
7
7
5
5
-7
-7
-6
-6
6
6
-5
-5
Answers
GPT-4o mini
To solve the equation \( 3.75 \times 10^? = 0.0000375 \), we need to express \( 0.0000375 \) in scientific notation.
First, we recognize that \( 0.0000375 \) can be expressed as:
\[
0.0000375 = 3.75 \times 10^{-5}
\]
We can verify this:
- Move the decimal point in \( 3.75 \) left 5 times to convert it to \( 0.0000375 \).
Now we equate the two expressions:
\[
3.75 \times 10^? = 3.75 \times 10^{-5}
\]
Since both sides have \( 3.75 \), we can simplify by removing it from both sides:
\[
10^? = 10^{-5}
\]
Therefore, \( ? = -5 \).
Thus, the correct answer is:
**-5**
First, we recognize that \( 0.0000375 \) can be expressed as:
\[
0.0000375 = 3.75 \times 10^{-5}
\]
We can verify this:
- Move the decimal point in \( 3.75 \) left 5 times to convert it to \( 0.0000375 \).
Now we equate the two expressions:
\[
3.75 \times 10^? = 3.75 \times 10^{-5}
\]
Since both sides have \( 3.75 \), we can simplify by removing it from both sides:
\[
10^? = 10^{-5}
\]
Therefore, \( ? = -5 \).
Thus, the correct answer is:
**-5**