Question

Compare  7.6 × 10−25  and  6.7 × 10−52 . Which statement is true?(1 point)Responses7.6 × 10−25 < 6.7 × 10−527.6 times 10 Superscript negative 25 Baseline is less than 6.7 times 10 Superscript negative 52 Baseline7.6 × 10−25 = 6.7 × 10−527.6 times 10 Superscript negative 25 Baseline equals 6.7 times 10 Superscript negative 52 Baseline7.6 × 10−25 > 6.7 × 10−527.6 times 10 Superscript negative 25 Baseline is greater than 6.7 times 10 Superscript negative 52 Baseline7.6 × 10−25 ≤ 6.7 × 10−52

Answer 1

To compare the numbers \(7.6 \times 10^{-25}\) and \(6.7 \times 10^{-52}\), we can convert both numbers to a similar power of ten. Since the powers of ten differ significantly, it’s easier to convert \(7.6 \times 10^{-25}\) to a form with the same exponent as \(6.7 \times 10^{-52}\).

1. Rewrite \(7.6 \times 10^{-25}\):
\[
7.6 \times 10^{-25} = 7.6 \times 10^{-25 + 27} = 7.6 \times 10^{2} \times 10^{-52} = 760 \times 10^{-52}
\]

Now we have:
\[
760 \times 10^{-52} \text{ and } 6.7 \times 10^{-52}
\]

2. Compare the coefficients:
\[
760 \text{ (from } 7.6 \times 10^{-25}) \text{ vs } 6.7 \text{ (from } 6.7 \times 10^{-52})
\]

Since \(760 > 6.7\), we can conclude:
\[
7.6 \times 10^{-25} > 6.7 \times 10^{-52}
\]

Therefore, the true statement is:
**7.6 times 10 Superscript negative 25 Baseline is greater than 6.7 times 10 Superscript negative 52 Baseline.**