Math.8.NS.1 8.NS.A.1 Math.8.NS.2 8.NS.A.2

Common Core Standards Real Numbers
Grade:	8th Grade
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:	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.

8th Grade Math - Real Numbers Lesson

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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

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.

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