Final answer:
To estimate the expression 210 ÷ 5.2 . 9 3/4 +(-205), we first simplify it to an approximation of 204.5. This estimation involves basic arithmetic and rounding according to significant figures, with adjustments based on the precision of the values in the expression.
Step-by-step explanation:
The question involves estimating a mathematical expression using significant figures and basic arithmetic operations. First, let's estimate 210 ÷ 5.2. Since 5.2 is approximately 5, we can say that 210 ÷ 5 is about 42. Next, we need to multiply this approximation by 9 3/4, which is 9.75 in decimal form. Multiplying 42 by 9.75 gives us approximately 409.5. Finally, let's add (-205) to our result. Adding -205 to 409.5 gives us an estimated total of 204.5.
When dealing with rounding and significant figures, we should pay attention to the context and precision required for the result. An answer like 204.5 may need to be rounded depending on the precision of the numbers provided in the expression. For instance, if only two significant figures are appropriate, we would round 204.5 to 200 since the first dropped digit (4) is less than 5.
If we had the detailed information about all the numbers in the list provided and their relation to the calculation, we could further refine our reasoning about significant figures and rounding. However, without additional context, we use the basic concepts of significant figures and arithmetic to estimate and round the answer.
Additionally, as noted in the hint provided, comparing the result ratio of the original problem with a percentage change like from 2.3% to 2.9% could help assess the reasonability of time-related estimates in a different context.