To compare \(7.6 \times 10^{-25}\) and \(6.7 \times 10^{-52}\), we can focus on the powers of ten first, as they determine the order of magnitude.
- The first number is \(7.6 \times 10^{-25}\).
- The second number is \(6.7 \times 10^{-52}\).
Since \(-25\) is greater than \(-52\), \(10^{-25}\) is greater than \(10^{-52}\).
Now we can express both numbers in terms of a common power of ten to make the comparison clearer. We can rewrite \(6.7 \times 10^{-52}\) to have the same power of ten as the first number:
\[ 6.7 \times 10^{-52} = 6.7 \times 10^{-52 + 25} \times 10^{-25} = 6.7 \times 10^{-27} \times 10^{-25} \]
So now we have:
- \(7.6 \times 10^{-25}\)
- \(6.7 \times 10^{-27} \times 10^{-25} = 0.00000000067 \times 10^{-25}\)
Now, we can compare:
\(7.6 \text{ (as a decimal)}\) versus \(0.00000000067 \text{ (as a decimal)}\).
Clearly, \(7.6\) is much greater than \(0.00000000067\).
Thus, we conclude that:
\[ 7.6 \times 10^{-25} > 6.7 \times 10^{-52} \]
Therefore, the true statement is \(7.6 \times 10^{-25}\) is greater than \(6.7 \times 10^{-52}\).