Final answer:
The number 4000 has one significant figure, while the number 400 must have two significant figures, as evidenced by the three significant figures in the quotient 10.0. The number 400 is best represented as 4.0 x 10² in scientific notation for clarity.
Step-by-step explanation:
When evaluating the significant figures in the equation 4000/400 = 10.0, we must look at the significant figures in the result and apply the rules of significant figures to the numbers used in the calculation. We see that the result is stated as 10.0, which has three significant figures.
According to the rules of significant figures, trailing zeros in a number are significant only if they are after a decimal point or if the number is written in scientific notation. Therefore, the number 4000 has one significant figure because the trailing zeros do not come after a decimal point and serve as place keepers. However, the number 400 must have two significant figures because if it had one significant figure like 4000, the division would yield a maximum of one significant figure in the answer, which contradicts the three significant figures present in 10.0.
To express the number 400 with two significant figures and avoid ambiguity, it should be written in scientific notation as 4.0 x 102.