Final answer:
The number of zeros at the end of 51! - 50! is one. This is because 50! is common to both terms, and 50 × 50! contributes exactly one zero at the end after subtraction.
Step-by-step explanation:
The number of zeros at the end of the expression 51! - 50! can be determined by understanding the properties of factorials. The factorial of a number n, denoted by n!, is the product of all positive integers less than or equal to n. Therefore, 51! is 51 × 50 × 49 × … × 1 and 50! is 50 × 49 × … × 1. We can see that 50! is a common factor in both terms:
51! - 50! = 51 × 50! - 1 × 50! = (51 - 1) × 50! = 50 × 50!
By looking at 50 × 50!, the only factor of 10 is the 50 itself (which is 5 × 10), which means there is only one zero at the end of the expression. Any other multiplication by numbers in 50! that contributes zeros is subtracted out when we subtract 50! from 51! × 50!, leaving only the one zero contribution from the 50 in 50 × 50!.
Since neither 51! nor 50! has a decimal point, the concept of significant figures does not directly apply here when counting zeros at the end of the number. Hence, we don't need to consider significant figures, and the final answer doesn't change regardless of the number of significant figures in the original terms.