Compare Very Large and Very Small Numbers Quick Check

Question

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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 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 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 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 note the following:

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

Since \(-25\) is greater than \(-52\), we know that \(10^{-25}\) is a larger number than \(10^{-52}\). Thus, \(7.6 \times 10^{-25}\) is larger than \(6.7 \times 10^{-52}\) because the 7.6 is multiplied by a larger power of ten.

Therefore, the correct statement is:

7.6 × 10⁻²⁵ > 6.7 × 10⁻⁵²