Question

Which sign makes the statement true?
765,680,000,000 * 10^-36 7.6568 * 10^26
><=

Answer 1

To determine the correct sign (either >, <, or =) between the two values \( 765,680,000,000 \times 10^{-36} \) and \( 7.6568 \times 10^{26} \), we need to rewrite the first number in scientific notation.

First, we express \( 765,680,000,000 \) in scientific notation:

\[
765,680,000,000 = 7.6568 \times 10^{11}
\]

Now let's multiply this by \( 10^{-36} \):

\[
7.6568 \times 10^{11} \times 10^{-36} = 7.6568 \times 10^{11 - 36} = 7.6568 \times 10^{-25}
\]

Now we have:

- \( 765,680,000,000 \times 10^{-36} = 7.6568 \times 10^{-25} \)
- \( 7.6568 \times 10^{26} \)

Now we compare \( 7.6568 \times 10^{-25} \) and \( 7.6568 \times 10^{26} \):

Since \( 10^{-25} \) is much smaller than \( 10^{26} \), we know that:

\[
7.6568 \times 10^{-25} < 7.6568 \times 10^{26}
\]

Thus, the correct sign is:

\[
7.6568 \times 10^{-25} < 7.6568 \times 10^{26}
\]

So the answer is:

\[
\boxed{<}
\]