State true or false. All decimal numbers are also rational numbers.

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True

False

answer is A.

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Detailed Solution

The statement says that all decimal numbers are rational numbers and we have to decide if this is true or not.
Now, as per the definition, a rational number is of a fraction or a ratio of two integers, i.e.,

p q

, where p and q are integers and q is always positive and non-zero.
Also, it is a fact that every decimal number can be expressed as a fraction by shifting the decimals to the right of the given number till it becomes an integer and introducing a denominator with as much power of 10 as the number of places the decimal point shifts.
Example-

0.4 = 410 = 25

So, we conclude that any decimal can be expressed as a fraction and so all decimal numbers are also rational numbers.
Hence, the statement is true.
Hence the correct option is (1).

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