F.2 Mathematics ---Approximation and Errors

用戶96740

2008-08-19 11:37 pm

Given a four-dight odd number which is greater than 9000 and is divisible by 13. When rounded off to 3 significant figures, it si divisible by 4. When rounded off to 2 significant figures, it is divisible by 11. Find the number.

Please help me to solve this problem and tell me the solutions with clear explaination.

Thanks!

回答 (1)

Uncle Michael

2008-08-20 12:20 am

✔ 最佳答案

The number is 9919.

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Reasons:

The four-digit number is greater than 9000.
Hence, the number should be 9???.

When the number is round off to 2 significant figures,
it is divisible by 11.
The rounded off number should be 9900.
Hence, the number should be between 9850 and 9949 inclusively.

The four-digit odd numbers between 9850 and 9949 inclusively that
can be divisble by 11 are:
9867, 9893, 9919, 9945

When rounded off to 3 significant figures:
9867 becomes 9870, which is NOT divisible by 4.
9893 becomes 9890, which is NOT divisible by 4.
9919 becomes 9920, which IS divisible by 4.
9945 becomes 9950, which is NOT divisible by 4.

Hence, the number is 9919.
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