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Is 5.1005.100 a rational number?\newlineChoices:\newline(A) yes\newline(B) no

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Identify rational and irrational numbersright chevron icon

Full solution

Q. Is 5.1005.100 a rational number?\newlineChoices:\newline(A) yes\newline(B) no
  1. Analyze number 5.1005.100: Step 11: Analyze the number 5.1005.100.\newline5.1005.100 has three digits after the decimal point and it terminates.
  2. Determine terminating decimal: Step 22: Determine if 5.1005.100 is a terminating decimal.\newlineSince 5.1005.100 can be expressed as 5.1001\frac{5.100}{1} or 51001000\frac{5100}{1000} after simplifying, it is a terminating decimal.
  3. Define rational irrational numbers: Step 33: Define rational and irrational numbers.\newlineA rational number can be expressed as a fraction with integers in the numerator and a non-zero integer in the denominator. An irrational number cannot be expressed this way.
  4. Check rational number definition: Step 44: Check if 5.1005.100 fits the definition of a rational number.\newlineSince 5.1005.100 is a terminating decimal, it can be expressed as a fraction (5100/1000)(5100/1000), which simplifies to 51/1051/10. Both 5151 and 1010 are integers, and 1010 is not zero.

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