Compare 7.6 × 10−25 and 6.7 × 10−52 . Which statement is true?

1 answer

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.

  1. The first number is \(7.6 \times 10^{-25}\).
  2. 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 \(6.7 \times 10^{-52}\).