Question

Question Compare 7.6 × 10−25 and 6.7 × 10−52 . Which statement is true?(1 point) Responses 7.6 × 10−25 > 6.7 × 10−52 7.6 times 10 Superscript negative 25 Baseline is greater than 6.7 times 10 Superscript negative 52 Baseline 7.6 × 10−25 < 6.7 × 10−52 7.6 times 10 Superscript negative 25 Baseline is less than 6.7 times 10 Superscript negative 52 Baseline 7.6 × 10−25 ≤ 6.7 × 10−52 7.6 times 10 Superscript negative 25 Baseline is less than or equal to 6.7 times 10 Superscript negative 52 Baseline 7.6 × 10−25 = 6.7 × 10−52

Answer 1

To compare the two numbers \( 7.6 \times 10^{-25} \) and \( 6.7 \times 10^{-52} \), we can analyze the scientific notation.

1. The first part of the numbers (the coefficients) are \( 7.6 \) and \( 6.7 \).
2. The exponent parts are \( -25 \) and \( -52 \).

Since the exponent \( -25 \) is greater than \( -52 \) (meaning it is closer to zero), \( 10^{-25} \) represents a larger number than \( 10^{-52} \).

To make the comparison easier, we can express both terms to the same exponent:

\[
7.6 \times 10^{-25} = 7.6 \times 10^{-25}
\]

\[
6.7 \times 10^{-52} = 6.7 \times 10^{-52} \times \frac{10^{27}}{10^{27}} = 6.7 \times 10^{-25} \times 10^{-27} = 6.7 \times 10^{-25} \times 0.0000000000000000000000001
\]

Since \( 10^{27} \) is a very small number, we can state that:
\[
6.7 \times 10^{-52} \text{ is significantly smaller than } 7.6 \times 10^{-25}
\]

Thus, the comparison can be concluded as:

\[
7.6 \times 10^{-25} > 6.7 \times 10^{-52}
\]

The correct statement is:
**7.6 × 10^(-25) > 6.7 × 10^(-52)**.