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

Question

GPT-4o mini · Answer

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} $.