Question
What power of 10 would make the following equation true?
3.75*10^? = 0.0000375
6
5
-7
-5
-6
7
3.75*10^? = 0.0000375
6
5
-7
-5
-6
7
Answers
GPT-4o mini
To determine the power of 10 that makes the equation \( 3.75 \times 10^{?} = 0.0000375 \) true, we can first express \( 0.0000375 \) in scientific notation.
To convert \( 0.0000375 \) into scientific notation:
- Move the decimal point 5 places to the right, which gives us \( 3.75 \).
- Because we moved the decimal to the right, we need to use a negative exponent of \( -5 \) to represent the original number:
\[
0.0000375 = 3.75 \times 10^{-5}
\]
Now, we set up the equation:
\[
3.75 \times 10^{?} = 3.75 \times 10^{-5}
\]
Since the coefficients (3.75) are the same, we can equate the powers of 10:
\[
? = -5
\]
Thus, the power of 10 that makes the equation true is:
\(-5\)
To convert \( 0.0000375 \) into scientific notation:
- Move the decimal point 5 places to the right, which gives us \( 3.75 \).
- Because we moved the decimal to the right, we need to use a negative exponent of \( -5 \) to represent the original number:
\[
0.0000375 = 3.75 \times 10^{-5}
\]
Now, we set up the equation:
\[
3.75 \times 10^{?} = 3.75 \times 10^{-5}
\]
Since the coefficients (3.75) are the same, we can equate the powers of 10:
\[
? = -5
\]
Thus, the power of 10 that makes the equation true is:
\(-5\)