Questions and Answers
The sum of a rational number and an irrational number equals:
an irrational number.
Which fraction has a repeating decimal as its decimal expansion?
3/11
What is the sum and classification of 3/20 + 10?
3.31227766..., irrational
Which is the decimal expansion of 7/22?
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Which is the correct classification of 18?
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The repeating decimal 0.27 is converted to the fraction 0.27 = 3/x. What is the value of x in the fraction?
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Which irrational number can be added to get a sum that is rational?
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How many repeating digits are in 0.536?
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Study Notes
Rational and Irrational Numbers
- The sum of a rational number and an irrational number results in an irrational number.
- A fraction presenting a repeating decimal is 3/11.
Decimal Expansions
- The sum of fractions like 3/20 and whole numbers (10), results in an irrational number with a decimal approximation of 3.31227766...
- The decimal expansion of the fraction 7/22 is approximately 0.318, denoting it as a repeating decimal.
Classification of Numbers
- The whole number 18 is classified incorrectly in the context; it is a rational, non-repeating integer rather than an irrational number.
- The repeating decimal 0.27 can be expressed as the fraction 3/x, where x equals 11.
Manipulating Irrational Numbers
- To obtain a rational result from adding an irrational number, one can add its negative counterpart (e.g., -r).
Decimal Repetition
- The decimal 0.536 contains three repeating digits.
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Description
Test your knowledge on rational and irrational numbers, including their properties, decimal expansions, and classifications. This quiz covers concepts like sums of numbers and the representation of repeating decimals. Perfect for students looking to strengthen their understanding of number theory.
