Questions and Answers
Which is the correct classification of 0.375?
Which correctly uses bar notation to represent the repeating decimal for 6/11?
How many repeating digits are in the conversion of a repeating decimal to a fraction?
Is Manda correct in converting the following repeating decimal to a fraction? What was her mistake?
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Which is the correct classification of a nonrepeating decimal?
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Which numbers are irrational? Select all that apply.
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Find the sum of 2.9580398... and 8.0467384..., then classify it.
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Which expressions represent rational numbers? Select all that apply.
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Find the sum of 9.58297100... and another rational number, then classify it.
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Explain how to distinguish between a rational number and an irrational number.
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Can the product of two irrational numbers be rational? Explain your answer and support with an example.
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Study Notes
Classification of Numbers
- Irrational Number: Cannot be expressed as a fraction; examples include non-repeating, non-terminating decimals.
- Rational Number: Can be expressed as a fraction, including terminating or repeating decimals, e.g., 0.375 is a rational number.
Bar Notation
- Bar notation is used to indicate repeating decimals.
- For the fraction 6/11, 0.54^- correctly uses bar notation to show that "54" repeats.
Converting Repeating Decimals
- To convert a repeating decimal to a fraction, identify the number of repeating digits.
- Example: For een repeating decimal, there are 2 repeating digits and multiplying both sides by 100 helps form the correct equation.
Evaluating Conversion Work
- Analyzing Manda's conversion, she made an error by not subtracting one x from the left side in her calculations.
Classification Examples
- Irrational Numbers: Non-repeating decimals are considered irrational.
- A number must have certain characteristics to be classified correctly as rational or irrational.
Identifying Irrational Numbers
- Selection of irrational numbers can be tested; examples labeled as B, E, and F from a given list were determined to be irrational.
Summing and Classifying
- The sum of numbers like 2.9580398... (irrational) + 8.0467384... (irrational) + 8.75 (rational) yields 8.75, which is rational since it can be expressed as a fraction.
Rational Number Expressions
- Expressions that qualify as rational numbers can be identified and specifically are A, B, C, and F.
Additional Sums and Classifications
- Similar to previous examples, sums involving both irrational and rational numbers help in identifying resulting classifications. The sum of 10.3727253... is classified as irrational.
Distinguishing Rational and Irrational Numbers
- Rational numbers can be whole numbers, fractions, or decimals with terminating/repeating digits.
- The square root of a perfect square is rational; otherwise, the number is irrational.
Products of Irrational Numbers
- The product of two irrational numbers can be rational, particularly when a non-perfect square's square root is squared (e.g., √5 × √5 = 5, which is rational).
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Description
Test your knowledge about real numbers with these flashcards. This quiz includes questions on rational and irrational numbers, as well as the use of bar notation for repeating decimals. Perfect for students needing a quick review or preparation for exams.
