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
3.75×10?=0.0000375
(1 point)
Responses
-7
-7
5
5
7
7
-6
-6
6
6
-5
Answers
GPT-4o mini
To solve for the power of 10 that makes the equation \( 3.75 \times 10^? = 0.0000375 \) true, we can start by rewriting \( 0.0000375 \) in scientific notation.
1. Convert \( 0.0000375 \) into scientific notation:
- Move the decimal point 5 places to the right to express it as \( 3.75 \).
- This gives us:
\[
0.0000375 = 3.75 \times 10^{-5}
\]
2. Now, we can rewrite the original equation using this new expression:
\[
3.75 \times 10^? = 3.75 \times 10^{-5}
\]
3. Since the coefficients (3.75) on both sides of the equation are equal, we can set the powers of 10 equal to each other:
\[
? = -5
\]
Therefore, the power of 10 that makes the equation true is \(-5\).
The correct response is:
\(-5\)
1. Convert \( 0.0000375 \) into scientific notation:
- Move the decimal point 5 places to the right to express it as \( 3.75 \).
- This gives us:
\[
0.0000375 = 3.75 \times 10^{-5}
\]
2. Now, we can rewrite the original equation using this new expression:
\[
3.75 \times 10^? = 3.75 \times 10^{-5}
\]
3. Since the coefficients (3.75) on both sides of the equation are equal, we can set the powers of 10 equal to each other:
\[
? = -5
\]
Therefore, the power of 10 that makes the equation true is \(-5\).
The correct response is:
\(-5\)