On rounding off a number to the nearest hundred as well as nearest thousand, we get 47,000. Which of the following could be the number?
Answer (2)
Determine the range for a number that rounds to 47,000 when rounded to the nearest hundred: 46950 ≤ x < 47050 .
Determine the range for a number that rounds to 47,000 when rounded to the nearest thousand: 46500 ≤ x < 47500 .
Find the intersection of these two ranges: 46950 ≤ x < 47050 .
Any number within the range 46950 ≤ x < 47050 could be the original number.
Explanation
Problem Analysis Let's analyze the problem. We need to find a number that rounds to 47,000 when rounded to the nearest hundred and to the nearest thousand. This means the number must fall within certain ranges for both rounding conditions to be met.
Range for Rounding to Nearest Hundred A number rounds to 47,000 when rounded to the nearest hundred if it is between 46,950 and 47,049.999... In mathematical terms, this can be written as 46950 ≤ x < 47050 .
Range for Rounding to Nearest Thousand A number rounds to 47,000 when rounded to the nearest thousand if it is between 46,500 and 47,499.999... In mathematical terms, this can be written as 46500 ≤ x < 47500 .
Finding the Intersection of the Ranges Now, we need to find the intersection of these two ranges. That is, we need to find the numbers that satisfy both conditions. The intersection of 46950 ≤ x < 47050 and 46500 ≤ x < 47500 is 46950 ≤ x < 47050 .
Possible Numbers Any number within the range 46950 ≤ x < 47050 will round to 47,000 when rounded to the nearest hundred and to the nearest thousand.
Final Answer Therefore, any number in the range 46950 ≤ x < 47050 could be the original number.
Examples
Rounding is a common practice in everyday life. For example, if you have a collection of 46,980 stamps, you might say you have approximately 47,000 stamps when speaking casually. Similarly, if a stadium holds 47,020 people, it's often rounded to 47,000 for simplicity. This helps in quick estimations and communications where exact numbers aren't necessary.
A number that rounds to 47,000 when rounded to the nearest hundred must fall between 46,950 and 47,049.999..., while for the nearest thousand, it must be between 46,500 and 47,499.999.... The overlapping range is 46,950 to 47,049, indicating that any number within this range could be the original number.
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