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

3 answers

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:

\[ 10^{-4} \]

u sure

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.

  1. 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!