(a) About 8,000 people attended a baseball game. If this figure has been rounded to the nearest

step 1 You have a ballpark estimate for the number of seats in a typical major league ballpark. Well, y

(a) About 8,000 people attended a baseball game. If this...

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Key Concepts

Rounding to the Nearest Thousand

This concept involves approximating a number by replacing it with the closest multiple of 1,000. The process takes into account the value of the hundreds digit and follows standard rounding rules, where values exactly halfway between two multiples (typically at the 500 mark) are rounded upward. This ensures the rounded number represents the original number within a certain margin of error.

Rounding Error Margin

Rounding introduces an error margin, which is typically half of the rounding unit. When a number is rounded to the nearest thousand, the error margin is 500. This means the actual number could be as low as 500 less or as high as 500 more than the multiple of 1,000 to which it was rounded, defining an interval within which the true value lies.

Determining Error Intervals

To find the range of possible actual values after rounding, one subtracts the rounding error (in this case, 500) from the rounded number to find the lower bound and adds the same error to find the upper bound. This interval encapsulates all numbers that would round to the provided approximation, highlighting an important aspect of approximation in mathematics.

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