Compare 7.6 × 10−25

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 equals 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)

GPT-4o mini · Answer

To compare the two numbers $7.6 \times 10^{-25}$ and $6.7 \times 10^{-52}$, we need to analyze their magnitudes, particularly focusing on the powers of ten, as they represent very small values. 1. **Scientific notation** indicates that the number is represented in the form of $a \times 10^b$, where $a$ is a coefficient and $b$ is the exponent. 2. Looking at the two numbers: - $7.6 \times 10^{-25}$ - $6.7 \times 10^{-52}$ 3. The exponent of $10^{-25}$ is higher (less negative) than the exponent of $10^{-52}$. This means that $10^{-25}$ is larger than $10^{-52}$. 4. Now we can compare the two numbers: - Since $7.6$ is positive and $10^{-25}$ is larger than $10^{-52}$, the entire value of $7.6 \times 10^{-25}$ will be greater than $6.7 \times 10^{-52}$. Thus, the correct statement is: **7.6 × 10−25 > 6.7 × 10−52**.