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Mathematics > Grade 8 > The Number System
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Mathematics | Grade : 8

Domain - The Number System

Cluster - Know that there are numbers that are not rational, and approximate them by rational numbers.

[8.NS.A.1] - Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Resources:


  • Decimal expansion
    Writing a rational number as a decimal.
  • Irrational number
    A number that cannot be expressed as a quotient of two integers, e.g.,√2 . It can be shown that a number is irrational if and only if it cannot be written as a repeating or terminating decimal.
  • Rational number
    A number expressible in the form a∕b or – a∕b for some fraction a∕b. The rational numbers include the integers.
  • Repeating decimal
    A decimal in which, after a certain point, a particular digit or sequence of digits repeats itself indefinitely; the decimal form of a rational number.

Predecessor Standards:

  • 7.NS.A.2.d
    Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Successor Standards:

  • AI.N-RN.B.3
    Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
  • AII.A-APR.D.6
    Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
  • MII.N-RN.B.3
    Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
  • MIII.A-APR.D.6
    Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Same Level Standards:

  • 8.NS.A.2
    Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g.,π2). For example, by truncating the decimal expansion of √2 show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
  • 8.EE.A.2
    Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.