Compare 7.6 × 10 to the power of −25 and 6.7 × 10 to the power of −52 . Which statement is true?(1 point)

Question

Responses

7.6 × 10 to the power of −25 > 6.7 × 10 to the power of −52
7.6 times 10 Superscript negative 25 Baseline is greater than 6.7 times 10 Superscript negative 52 Baseline

7.6 × 10 to the power of −25 < 6.7 × 10 to the power of −52
7.6 times 10 Superscript negative 25 Baseline is less than 6.7 times 10 Superscript negative 52 Baseline

7.6 × 10 to the power of −25 = 6.7 × 10 to the power of −52
7.6 times 10 Superscript negative 25 Baseline equals 6.7 times 10 Superscript negative 52 Baseline

7.6 × 10 to the power of −25 ≤ 6.7 × 10 to the power of −52

Answer 1

To compare \( 7.6 \times 10^{-25} \) and \( 6.7 \times 10^{-52} \), we can compare their values by first noting the exponent of 10.

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

Since both numbers are in scientific notation, we can analyze their exponents:

• The exponent \(-25\) is greater than \(-52\).

This means that \( 10^{-25} \) is significantly larger than \( 10^{-52} \).

Now let's compare combining the coefficients:

• \(7.6 \times 10^{-25}\) can be thought of as \(7.6\) multiplied by a larger number compared to \(6.7 \times 10^{-52}\), which is effectively \(6.7\) multiplied by a much smaller number.

Thus, \( 7.6 \times 10^{-25} \) is indeed greater than \( 6.7 \times 10^{-52} \).

The true statement is:

7.6 × 10 to the power of −25 > 6.7 × 10 to the power of −52.