Compare 7.6 × 10^-²⁵ and 6.7 × 10^-⁵². Which statement is true?
A. 7.6 × 10^-²⁵ < 6.7 × 10^-⁵²
B. 7.6 × 10^-²⁵ ≤ 6.7 × 10^-⁵²
C. 7.6 × 10^-²⁵ = 6.7 × 10^-⁵²
D. 7.6 × 10^-²⁵ > 6.7 × 10^-⁵²
The expression "7.6 × 10^-²⁵" represents a very small decimal number, as it is multiplied by a negative exponent. The expression "6.7 × 10^-⁵²" represents an even smaller decimal number because it is multiplied by a larger negative exponent.
Since the second expression represents an even smaller number than the first expression, the correct statement is:
A. 7.6 × 10^-²⁵ < 6.7 × 10^-⁵²
To compare the two numbers:
1. Bring both numbers to the same power of 10 by adjusting the exponent:
7.6 × 10^-²⁵ = (7.6 × 10^-²⁵) × (10^⁵² ÷ 10^⁵²)
= 7.6 × (10^-²⁵ × 10^⁵²)
= 7.6 × 10^(-²⁵ + ⁵²)
= 7.6 × 10^²⁷
2. Now we can directly compare the two numbers:
7.6 × 10^²⁷ vs 6.7 × 10^-⁵²
Since the exponent of 7.6 × 10^²⁷ is positive and the exponent of 6.7 × 10^-⁵² is negative, we can conclude that 7.6 × 10^²⁷ is greater than 6.7 × 10^-⁵².
Therefore, the statement "7.6 × 10^-²⁵ > 6.7 × 10^-⁵²" is true. So the correct answer is D.
To compare the numbers 7.6 × 10^-²⁵ and 6.7 × 10^-⁵², we can compare their exponents and use the rules of scientific notation.
The first number, 7.6 × 10^-²⁵ can be written as 0.76 × 10^(-²⁵ + 1), which is equal to 0.76 × 10^-²⁴.
The second number, 6.7 × 10^-⁵² can be written as 0.67 × 10^(-⁵² + 1), which is equal to 0.67 × 10^-⁵¹.
Now, we can compare the two numbers directly:
0.76 × 10^-²⁴ < 0.67 × 10^-⁵¹
Since the exponent of 10 is very small in the second number, it means that the second number is a much smaller value compared to the first number.
Therefore, the correct statement is: A. 7.6 × 10^-²⁵ < 6.7 × 10^-⁵².