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Question

What are the different possible decimal expansions that you can expect when you divide any integer with 3?

A
0,0.33,0.666....
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B
0,0.3,0.6
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C
0,0.33,0.5
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D
0.33,0.5
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Solution

The correct option is A 0,0.33,0.666....
1. When the integer is divisible by 3, the decimal expansion will terminate in 0 i.e. the integer is divisible by 3.

2. Let's divide 1 by 3. We get:


3. Let's divide 2 by 3. We get:


Hence, if any integer is divided by 3, there are 3 possibilities:
1. The decimal expansion will terminate.
2. The decimal expansion will have 3 repeating.
3. The decimal expansion will have 6 repeating.

Hence, option A is correct.

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