## Standards with the same topic and subject but for other grades

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

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.

Understand subtraction of rational numbers as adding the additive inverse, π± β π² = π± + (βπ²). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Describe situations in which opposite quantities combine to make 0.

Understand π± + π² as the number located a distance |π²| from π±, in the positive or negative direction depending on whether π² is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If π± and π² are integers, then β(π±/π²) = (βπ±)/π² = π±/(βπ²). Interpret quotients of rational numbers by describing real-world contexts.

Describe situations in which opposite quantities combine to make 0.

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., ΟΒ²).

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (β1)(β1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.