The Structure of Integers, Rational Numbers, and Absolute Value

Decompose natural numbers into prime factors using exponent notation and express numbers in expanded decimal form with powers of 10.

Model additive inverses, plot signed numbers on horizontal and vertical lines, and interpret absolute value as distance from zero.

Add and subtract signed fractions and decimals, interpret subtraction as adding the opposite, and calculate distance as |p - q|.

Multiply and divide signed fractions and decimals, understand the placement of negative signs in quotients, and convert fractions using long division.

Evaluate square and cube roots of perfect and non-perfect values, distinguish rational from irrational numbers, and convert repeating decimals to fractions.

Estimate the value of irrational square roots using rational bounds, place irrationals on number lines, and solve geometric radical problems.

Round numbers to specified decimal places or significant figures, check calculation reasonableness, and compute with scientific notation.

Solve complex, multi-step real-world problems combining fractions, decimals, signed numbers, exponents, and estimation.