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| Math Central | Quandaries & Queries |
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Question from Chris, a parent: I'm trying to help my daughter with this math question: Know the Numbers numbers 0 - 9 form a 4 digit number with no repetition. Change the number if you need to: It would round to 3000 if rounded to the nearest thousand The digit in the tens place is twice the value of the digit in the thousands place. It is an odd number. It contains the largest digit. It contains one digit less than 2. The digit in the hundreds place is odd. Can you find the 2 numbers? This is for a 6th grade quiz and I have no idea how to help her. Thanks! |
Hi Chris,
Since the number rounds to 3000 when rounded to the nearest thousand, the thousands digit must be 2 or 3. Suppose the thousands digit is 2 then the tens digit is 4 so the number is
2?4#
where ? and # are digits. One of these digits is the largest digit, 9, and the other is either 0 or 1. The number in the hundreds place, ?, is odd and the 4 digit number itself is odd so # is odd. Thus neither ? nor # can be 0. Hence the number is either
2149 or 2941.
Which one rounds to 3000 when rounded to the nearest thousand?
What happens if the thousands digit is 3?
Penny
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