Question

How many times less is 10^2 than 10^6? Express your answer as an integer power of 10.(1 point)
Responses

10,000
10,000

10−4
10 superscript negative 4 baseline

104
10 superscript 4 baseline

0.0001
0.0001

Answer 1

u sure

Answer 2

To find how many times less \(10^2\) is than \(10^6\), we can calculate the ratio of \(10^2\) to \(10^6\):

\[
\frac{10^2}{10^6}
\]

Using the properties of exponents, we can subtract the exponents:

\[
\frac{10^2}{10^6} = 10^{2-6} = 10^{-4}
\]

Thus, \(10^2\) is \(10^{-4}\) times less than \(10^6\).

The answer is:

\[
10^{-4}
\]

Answer 3

Yes, I am sure. Let's break it down step-by-step to confirm:

1. We want to determine how many times less \(10^2\) is than \(10^6\).

2. We calculate the ratio:

\[
\frac{10^2}{10^6}
\]

3. Using the exponent rule, where \(\frac{a^m}{a^n} = a^{m-n}\), we simplify this:

\[
\frac{10^2}{10^6} = 10^{2-6} = 10^{-4}
\]

This tells us that \(10^2\) is \(10^{-4}\) times \(10^6\), which means it is much smaller.

4. To express it clearly: \(10^2\) is \(1/10^4\) of \(10^6\), which confirms that it's \(10^{-4}\) times \(10^6\).

Therefore, the correct expression of how many times less \(10^2\) is than \(10^6\) is indeed:

\[
10^{-4}
\]

If you have any further questions or need clarifications, feel free to ask!