Real Numbers
8th Grade


Alabama Course of Study Standards:
1

Define the real number system as composed of rational and irrational numbers. Explain that every number has a decimal expansion; for rational numbers, the decimal expansion repeats or terminates.
 Convert a decimal expansion that repeats into a rational number.

Arkansas Academic Standards:
8.NS.A.1

Know that numbers that are not rational are called irrational: Understand that every number has a decimal expansion
For example: 2=2.00... Write a fraction a/b as a repeating decimal
 Write a repeating decimal as a fraction

Arizona Academic Standards:
8.NS.A.1

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion. Know that numbers whose decimal expansions do not terminate in zeros or in a repeating sequence of fixed digits are called irrational. 
Common Core State Standards:
Math.8.NS.1 or 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. 
Georgia Standards of Excellence (GSE):
8.NR.1.1

Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number. 
North Carolina  Standard Course of Study:
8.NS.1

Understand that every number has a decimal expansion. Building upon the definition of a rational number, know that an irrational number is defined as a nonrepeating, nonterminating decimal. 
New York State Next Generation Learning Standards:
8.NS.1

Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion eventually repeats. Know that other numbers that are not rational are called irrational. 
Alabama Course of Study Standards:
2

Locate rational approximations of irrational numbers on a number line, compare their sizes, and estimate the values
of the irrational numbers. 
Arkansas Academic 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., ^{2})
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. 
Arizona Academic 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 their values. 
Common Core State Standards:
Math.8.NS.2 or 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., ^{2}). 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.

Georgia Standards of Excellence (GSE):
8.NR.1.2

Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions. 
North Carolina  Standard Course of Study:
8.NS.2

Use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line. Estimate the value of expressions involving: Square roots and cube roots to the tenths.
 to the hundredths.

New York State Next Generation Learning Standards:
8.NS.2

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions. 
Wisconsin Academic 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, and estimate the value of expressions (e.g., ^{2}). 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. 
Pennsylvania Core Standards:
CC.2.1.8.E.1

Distinguish between rational and irrational numbers using their properties. 
Pennsylvania Core Standards:
M08.AN.1.1.1

Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths). 
Pennsylvania Core Standards:
M08.AN.1.1.2

Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths). 
Pennsylvania Core Standards:
CC.2.1.8.E.4

Estimate irrational numbers by comparing them to rational numbers. 
Pennsylvania Core Standards:
M08.AN.1.1.3

Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144). 
Pennsylvania Core Standards:
M08.AN.1.1.4

Use rational approximations of irrational numbers to compare and order irrational numbers. 
Pennsylvania Core Standards:
M08.AN.1.1.5

Locate/identify rational and irrational numbers at their approximate locations on a number line 
Florida  Benchmarks for Excellent Student Thinking:
MA.8.NSO.1.1

Extend previous understanding of rational numbers to define irrational numbers within the real number system. Locate an approximate value of a numerical expression involving irrational numbers on a number line. 
Florida  Benchmarks for Excellent Student Thinking:
MA.8.NSO.1.2

Plot, order and compare rational and irrational numbers, represented in various forms 
Georgia Standards of Excellence (GSE):
8.NR.1.1

Distinguish between rational and
irrational numbers using decimal
expansion. Convert a decimal
expansion which repeats eventually
into a rational number. 
Georgia Standards of Excellence (GSE):
8.NR.1.2

Approximate irrational numbers to
compare the size of irrational
numbers, locate them approximately
on a number line, and estimate the
value of expressions. 
