Question
What power of 10 would make the following equation true?
3.75×10?=0.0000375
(1 point)
Responses
5
5
6
6
-7
-7
-6
-6
-5
-5
7
3.75×10?=0.0000375
(1 point)
Responses
5
5
6
6
-7
-7
-6
-6
-5
-5
7
Answers
GPT-4o mini
To solve the equation \(3.75 \times 10^x = 0.0000375\), we need to express \(0.0000375\) in scientific notation.
First, let's rewrite \(0.0000375\):
- \(0.0000375\) can be written as \(3.75 \times 10^{-5}\) because moving the decimal point 5 places to the right converts it to \(3.75\).
Now, we can set up the equation:
\[
3.75 \times 10^x = 3.75 \times 10^{-5}
\]
Since the coefficients (3.75) are the same, we can equate the powers of 10:
\[
x = -5
\]
Therefore, the power of 10 that would make the equation true is \(-5\).
The answer is \(-5\).
First, let's rewrite \(0.0000375\):
- \(0.0000375\) can be written as \(3.75 \times 10^{-5}\) because moving the decimal point 5 places to the right converts it to \(3.75\).
Now, we can set up the equation:
\[
3.75 \times 10^x = 3.75 \times 10^{-5}
\]
Since the coefficients (3.75) are the same, we can equate the powers of 10:
\[
x = -5
\]
Therefore, the power of 10 that would make the equation true is \(-5\).
The answer is \(-5\).