Exploring Real Numbers Assignment Flashcards

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).