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Danielle claims that 7/8 is a rational number because it is a fraction whose decimal equivalent is a repeating decimal. is danielle's statement correct? why/why not?

User Krozero
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Final Answer:

Danielle's statement is incorrect. 7/8 is not a rational number because its decimal equivalent is a terminating decimal, which is a type of decimal that ends after a certain number of digits.

Step-by-step explanation:

A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. For example, 1/2, 3/4, and 5/6 are all rational numbers.

An irrational number is a number that cannot be expressed as a ratio of two integers. For example, √2, π, and e are all irrational numbers.

A repeating decimal is a decimal that has a pattern of digits that repeats indefinitely. For example, the decimal representation of 1/3 is 0.333333..., where the digit 3 repeats indefinitely.

A terminating decimal is a decimal that ends after a certain number of digits. For example, the decimal representation of 1/2 is 0.5, where the decimal ends after the digit 5.

Since the decimal representation of 7/8 is 0.875, which is a terminating decimal, 7/8 is a rational number. Danielle's statement that 7/8 is a rational number because it is a fraction whose decimal equivalent is a repeating decimal is incorrect.

User Bradrar
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