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Which of the following statements is true?Every irrational number can be represented as a fraction.Every irrational number can be represented with the help of decimals.Every rational number can be represented as a terminating decimal.Every rational number can be represented as an integer.

Question

Which of the following statements is true?Every irrational number can be represented as a fraction.Every irrational number can be represented with the help of decimals.Every rational number can be represented as a terminating decimal.Every rational number can be represented as an integer.

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Solution

The second and third statements are true.

Every irrational number can be represented with the help of decimals. Irrational numbers are numbers that cannot be expressed as a ratio of two integers, but they can be represented as non-terminating, non-repeating decimals.

Every rational number can be represented as a terminating decimal. Rational numbers are numbers that can be expressed as a ratio of two integers. When this ratio is converted to a decimal, it will either terminate (like 0.5 or 0.75) or repeat (like 0.333... or 0.666...).

The first statement is false. Irrational numbers cannot be represented as a fraction because by definition, they cannot be expressed as a ratio of two integers.

The fourth statement is also false. Not every rational number can be represented as an integer. For example, 1/2 is a rational number, but it is not an integer.

This problem has been solved

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