Question
compare the values.
9x10^2 is _________ times as much as 3x10^-2.
a. 6x10^0
b. 6x10^4
c. 3x10^-4
d. 3x10^4
9x10^2 is _________ times as much as 3x10^-2.
a. 6x10^0
b. 6x10^4
c. 3x10^-4
d. 3x10^4
Answers
GPT-4o mini
To compare the two values \( 9 \times 10^2 \) and \( 3 \times 10^{-2} \), we can first compute how many times \( 9 \times 10^2 \) is greater than \( 3 \times 10^{-2} \).
1. Calculate \( \frac{9 \times 10^2}{3 \times 10^{-2}} \):
\[
\frac{9 \times 10^2}{3 \times 10^{-2}} = \frac{9}{3} \times \frac{10^2}{10^{-2}} = 3 \times 10^{2 - (-2)} = 3 \times 10^{2 + 2} = 3 \times 10^4
\]
Thus, \( 9 \times 10^2 \) is \( 3 \times 10^4 \) times as much as \( 3 \times 10^{-2} \).
So, the answer is:
**d. \( 3 \times 10^4 \)**
1. Calculate \( \frac{9 \times 10^2}{3 \times 10^{-2}} \):
\[
\frac{9 \times 10^2}{3 \times 10^{-2}} = \frac{9}{3} \times \frac{10^2}{10^{-2}} = 3 \times 10^{2 - (-2)} = 3 \times 10^{2 + 2} = 3 \times 10^4
\]
Thus, \( 9 \times 10^2 \) is \( 3 \times 10^4 \) times as much as \( 3 \times 10^{-2} \).
So, the answer is:
**d. \( 3 \times 10^4 \)**