CC.2.1.8.E.1 Math.8.NS.1 8.NS.A.1 MA.8.NSO.1.1 MA.8.NSO.1.2 Math.8.NS.2 8.NS.A.2 M08.A-N.1.1.1 M08.A-N.1.1.2 CC.2.1.8.E.4 M08.A-N.1.1.3 M08.A-N.1.1.4 M08.A-N.1.1.5

Common Core Standards Real Numbers
Grade:	8th Grade
Standard:	CC.2.1.8.E.1
Description:	Distinguish between rational and irrational numbers using their properties.
Standard:	Math.8.NS.1 or 8.NS.A.1
Description:	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.
Standard:	MA.8.NSO.1.1
Description:	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.
Standard:	MA.8.NSO.1.2
Description:	Plot, order and compare rational and irrational numbers, represented in various forms
Standard:	Math.8.NS.2 or 8.NS.A.2
Description:	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.
Standard:	M08.A-N.1.1.1
Description:	Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths).
Standard:	M08.A-N.1.1.2
Description:	Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths).
Standard:	CC.2.1.8.E.4
Description:	Estimate irrational numbers by comparing them to rational numbers.
Standard:	M08.A-N.1.1.3
Description:	Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144).
Standard:	M08.A-N.1.1.4
Description:	Use rational approximations of irrational numbers to compare and order irrational numbers.
Standard:	M08.A-N.1.1.5
Description:	Locate/identify rational and irrational numbers at their approximate locations on a number line

A rational number can be written as a fraction

\frac{p}{q}

,
where p and q are integers and q does not equal zero.
Integers, fractions, and repeating decimals are rational numbers.

A real number that is not rational is irrational.
A decimal that does not terminate or repeat is irrational.

A rational number can be written as a fraction

\frac{p}{q}

, where p and q are integers and q does not equal zero.

0. \bar{9}

is a repeating decimal.

- 7

is an integer.

\sqrt{64} = 8

, which is an integer.

So,

0. \bar{9}, - 7,

and

\sqrt{64}

are rational numbers.

\frac{π}{3} = 1.0471 ...

, which is a non-terminating, non-repeating decimal.

\sqrt{92} = 9.5916 ...

, which is a non-terminating, non-repeating decimal.

So,

\frac{π}{3}

and

\sqrt{92}

are irrational numbers.

Common Core Standards

Real Numbers

CC.2.1.8.E.1

Distinguish between rational and irrational numbers using their properties.

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.

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.

MA.8.NSO.1.2

Plot, order and compare rational and irrational numbers, represented in various forms

Math.8.NS.2 or 8.NS.A.2

M08.A-N.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).

M08.A-N.1.1.2

Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths).

CC.2.1.8.E.4

Estimate irrational numbers by comparing them to rational numbers.

M08.A-N.1.1.3

Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144).

M08.A-N.1.1.4

Use rational approximations of irrational numbers to compare and order irrational numbers.

M08.A-N.1.1.5

Locate/identify rational and irrational numbers at their approximate locations on a number line

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