Question
Compare 7.6 x 10^-25 and 6.7 × 10^-52. Which statement is true?
7.6 × 10^-25 = 6.7 × 10^-32
7.6 × 10^-25 = 6.7 × 10^-32
Answers
GPT-4o mini
To compare \( 7.6 \times 10^{-25} \) and \( 6.7 \times 10^{-52} \), we need to consider the exponents of 10 and the coefficients.
1. The first number is \( 7.6 \times 10^{-25} \):
- The exponent is \(-25\).
2. The second number is \( 6.7 \times 10^{-52} \):
- The exponent is \(-52\).
Since \(-25\) is greater than \(-52\), we know that \( 10^{-25} \) is larger than \( 10^{-52} \).
Now we can compare the numbers:
- \( 7.6 \times 10^{-25} \) is a positive number multiplied by a larger power of ten compared to \( 6.7 \times 10^{-52} \), which means that \( 7.6 \times 10^{-25} \) is greater than \( 6.7 \times 10^{-52} \).
Thus, the following statement is true:
- \( 7.6 \times 10^{-25} > 6.7 \times 10^{-52} \).
Regarding the statement \( 7.6 \times 10^{-25} = 6.7 \times 10^{-32} \), this is incorrect because \( 6.7 \times 10^{-32} \) actually represents a different value than \( 7.6 \times 10^{-25} \).
1. The first number is \( 7.6 \times 10^{-25} \):
- The exponent is \(-25\).
2. The second number is \( 6.7 \times 10^{-52} \):
- The exponent is \(-52\).
Since \(-25\) is greater than \(-52\), we know that \( 10^{-25} \) is larger than \( 10^{-52} \).
Now we can compare the numbers:
- \( 7.6 \times 10^{-25} \) is a positive number multiplied by a larger power of ten compared to \( 6.7 \times 10^{-52} \), which means that \( 7.6 \times 10^{-25} \) is greater than \( 6.7 \times 10^{-52} \).
Thus, the following statement is true:
- \( 7.6 \times 10^{-25} > 6.7 \times 10^{-52} \).
Regarding the statement \( 7.6 \times 10^{-25} = 6.7 \times 10^{-32} \), this is incorrect because \( 6.7 \times 10^{-32} \) actually represents a different value than \( 7.6 \times 10^{-25} \).