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Question

Write the following rational number in decimal form and also state either it is terminating or non terminating, repeating decimal:
229400.

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Solution

The given rational number is 229400
To make simplification simple and easy, lets make the denominator multiples of 10.
Consider 229400
=2294×100
=22922×102
=229×5222×52×102 [ Multiplying 5252]
=5725102×102
=572510000
In the denominator, we have four zero's, so we need place the decimal point after 4 digits from right to left.
=0.5725
Hence, the decimal expansion is 0.5725.
Here, the decimal expansion terminates after finite number of steps.
229400 has a terminating decimal form.

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