Maths

• What is a terminating decimal?


  • A decimal that ends
  • Example: 0.75 from 3/4
• How can rational numbers be expressed?

  As fractions or terminating/recurring decimals
• What are rational numbers?

  Numbers expressible as fractions of whole numbers
• How can the whole number 5 be expressed as a rational number?

  As 5/1
• What is the fractional form of rational numbers?

  They can be written as a fraction
• What is a recurring decimal?

  • A decimal that repeats forever
  • Example: 0.666... from 2/3
• Which operations are rational numbers closed under?

  Addition, subtraction, multiplication, division
• What is the decimal representation of the fraction $\frac{3}{4}$?


  0.75
• How can rational numbers be represented?

  As fractions or terminating/recurring decimals
• What are irrational numbers?

  Numbers that cannot be written as fractions
• Why can't irrational numbers be expressed as fractions?

  They have non-repeating, non-ending decimal forms
• How do the decimal forms of irrational numbers differ from rational numbers?

  They are infinite and non-repeating.
• What is an exception to the closure property of rational numbers?

  Division by zero
• What are rational numbers?

  Numbers that can be expressed as fractions
• What are irrational numbers?

  Numbers that cannot be expressed as fractions
• What is the approximate value of π (pi)?

  ≈ 3.141592653...
• What is the approximate value of π (pi)?

  Approximately 3.14159
• What does the decimal approximation of √2 indicate about its nature?

  It goes on forever without repeating.
• What is the square root of 2 classified as?

  An irrational number
• What are the characteristics of irrational numbers?

  • Cannot be written as fractions
  • Decimal forms never end
  • Decimal forms do not repeat
• What is a defining characteristic of irrational numbers?

  They cannot be expressed as fractions.
• What does it mean for a rational number to be in decimal form?

  It either terminates or recurs
• What is the decimal representation of the fraction $\frac{2}{3}$?


  0.666...
• Why do irrational numbers have non-repeating decimals?

  Because they cannot be expressed as fractions
• What is the square root of 3 classified as?

  An irrational number
• How is π (pi) used in mathematics?

  To calculate the circumference of a circle
• Why are irrational numbers considered non-fractional?

  They cannot be expressed as a fraction of whole numbers.
• Why can irrational numbers not be expressed as simple fractions?

  • Their decimal representations go on forever
  • They do not repeat
  • They cannot be simplified to a fraction
• What is the approximate value of √3?

  Approximately 1.7320508
• Why is √2 considered an irrational number?

  It cannot be written as a fraction.
• What distinguishes rational numbers from irrational numbers in terms of their decimal representation?

  Rational numbers have terminating or recurring decimals
• Why is √2 considered an irrational number?

  It has a non-repeating, infinite decimal
• What are the properties of irrational numbers?

  • Non-fractional form: Cannot be expressed as a fraction.
  • Infinite decimals: Decimal forms never end and do not repeat.
  • Not closed: Adding or multiplying may yield rational or irrational results.
• What is the approximate value of √2?

  Approximately 1.41421356
• What is the definition of a rational number?

  Can be written as a fraction
• What is the definition of an irrational number?

  Cannot be written as a fraction
• What is the approximate value of √2?

  ≈ 1.414213562...
• Why is 3/4 considered a rational number?

  It equals 0.75, a terminating decimal
• What does closure under addition mean for rational numbers?

  Combining two rational numbers yields another rational number
• How does the decimal form of rational numbers differ from irrational numbers?

  Rational decimals terminate or recur