Peterson Hobbs
01/18/2023 · Senior High School
\( 9 \times 10^{2} \) is ? times as much as \( 3 \times 10^{-2} \). If
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find out how many times \( 9 \times 10^{2} \) is compared to \( 3 \times 10^{-2} \), we can set up the following calculation:
\[
\text{Ratio} = \frac{9 \times 10^{2}}{3 \times 10^{-2}}
\]
Now, we can simplify this expression step by step:
1. Divide the coefficients (the numbers in front):
\[
\frac{9}{3} = 3
\]
2. Now, divide the powers of ten:
\[
\frac{10^{2}}{10^{-2}} = 10^{2 - (-2)} = 10^{2 + 2} = 10^{4}
\]
3. Combine the results:
\[
\text{Ratio} = 3 \times 10^{4}
\]
Thus, \( 9 \times 10^{2} \) is \( 3 \times 10^{4} \) times as much as \( 3 \times 10^{-2} \).
In numerical form, \( 3 \times 10^{4} = 30000 \).
Therefore, \( 9 \times 10^{2} \) is **30,000 times** as much as \( 3 \times 10^{-2} \).
Quick Answer
\( 9 \times 10^{2} \) is 30,000 times as much as \( 3 \times 10^{-2} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit