Question
Compare 7.6×10 to the power of -25 and 6.7×10 with -52 power which statement is true would it be 7.6×10 with a -25 power equals 6.7×10 with the power of -52 or 7.6×10 with the power of -25 is less than 6.7×10 with the power of -52 or 7.6×10 with the power of -25 is greater than 6.7×10 with the power of -52 and last would it be 7.6×10 with the power of -25 is less than 6.7×10 with the power of -52
Answers
GPT-4o mini
To compare \( 7.6 \times 10^{-25} \) and \( 6.7 \times 10^{-52} \), we can consider the values of the numbers in scientific notation.
Both numbers are in the form \( a \times 10^b \), where \( a \) is the coefficient and \( b \) is the exponent.
1. **Understanding the numbers**:
- \( 7.6 \times 10^{-25} \) means \( 7.6 \) multiplied by \( 10^{-25} \) (a small number).
- \( 6.7 \times 10^{-52} \) means \( 6.7 \) multiplied by \( 10^{-52} \) (an even smaller number).
2. **Comparing the exponents**:
- The exponent of the first number is \(-25\).
- The exponent of the second number is \(-52\).
- Since \(-25\) is greater than \(-52\), \( 10^{-25} \) is larger than \( 10^{-52} \).
3. **Comparing the entire numbers**:
- To compare, we can express both numbers in a standard way. Since \( 10^{-25} \) is much larger than \( 10^{-52} \), we can rewrite \( 6.7 \times 10^{-52} \) in terms of \( 10^{-25} \):
\[
6.7 \times 10^{-52} = 6.7 \times 10^{-52 + 27} \times 10^{-25} = 6.7 \times 10^{-25} \times 10^{-27}
\]
- Since \( 10^{-27} \) is a very small factor, it shows how much smaller \( 6.7 \times 10^{-52} \) is compared to \( 7.6 \times 10^{-25} \).
Thus, we conclude that:
\[
7.6 \times 10^{-25} \text{ is greater than } 6.7 \times 10^{-52}
\]
The correct statement is:
- \( 7.6 \times 10^{-25} \) is greater than \( 6.7 \times 10^{-52} \).
Both numbers are in the form \( a \times 10^b \), where \( a \) is the coefficient and \( b \) is the exponent.
1. **Understanding the numbers**:
- \( 7.6 \times 10^{-25} \) means \( 7.6 \) multiplied by \( 10^{-25} \) (a small number).
- \( 6.7 \times 10^{-52} \) means \( 6.7 \) multiplied by \( 10^{-52} \) (an even smaller number).
2. **Comparing the exponents**:
- The exponent of the first number is \(-25\).
- The exponent of the second number is \(-52\).
- Since \(-25\) is greater than \(-52\), \( 10^{-25} \) is larger than \( 10^{-52} \).
3. **Comparing the entire numbers**:
- To compare, we can express both numbers in a standard way. Since \( 10^{-25} \) is much larger than \( 10^{-52} \), we can rewrite \( 6.7 \times 10^{-52} \) in terms of \( 10^{-25} \):
\[
6.7 \times 10^{-52} = 6.7 \times 10^{-52 + 27} \times 10^{-25} = 6.7 \times 10^{-25} \times 10^{-27}
\]
- Since \( 10^{-27} \) is a very small factor, it shows how much smaller \( 6.7 \times 10^{-52} \) is compared to \( 7.6 \times 10^{-25} \).
Thus, we conclude that:
\[
7.6 \times 10^{-25} \text{ is greater than } 6.7 \times 10^{-52}
\]
The correct statement is:
- \( 7.6 \times 10^{-25} \) is greater than \( 6.7 \times 10^{-52} \).