Free Printable WorksheetMathGrade 8Math Curriculum8.NS.A.1

8.2 Understanding Decimal Expansions of Rational Numbers Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.2 Understanding Decimal Expansions of Rational Numbers. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.2 Understanding Decimal Expansions of Rational Numbers - Which statement correctly describes the decimal expansion of a rational number (terminating or repeating) and its connection to fractions? (CCSS 8.NS.A.1; CA 8.NS.A.1; MA 8.NS.A.1)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 8

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 8.2 Understanding Decimal Expansions of Rational Numbers skill assessments:

Problem 1Difficulty: Hard
Which conclusion is justified about 0.124124124... and 0.1241241124...?
ABoth are rational because they both start with 124.
BThe first is rational because it repeats; the second is not shown repeating, so it should not be assumed rational.
CThe first is irrational and the second is rational.
DBoth terminate because they use only the digits 1, 2, and 4.
Solution & Explanation:0.124124124... clearly repeats the block 124, so it is rational. The second decimal does not show a fixed repeating block, so you cannot conclude it is rational.
Problem 2Difficulty: Hard
Which fraction and decimal match correctly?
A3/25 = 0.012
B5/6 = 0.8333...
C7/20 = 0.285714...
D11/8 = 0.11
Solution & Explanation:5/6 = 0.8333..., where the 3 repeats. The other pairs do not match the correct decimal values.
Problem 3Difficulty: Hard
Which number best shows an eventually repeating decimal with a nonrepeating start?
A0.583333...
B0.727272...
C0.625
D0.123456789101112...
Solution & Explanation:In 0.583333..., the digits start with 58 and then the 3s repeat. That is eventually repeating.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.NS.A.1 (Primary standard selected for prompt fields: CCSS 8.NS.A.1. Skill statement: Which statement correctly describes the decimal expansion of a rational number (terminating or repeating) and its connection to fractions? Associated standards listed with this skill: CCSS 8.NS.A.1; CA 8.NS.A.1; MA 8.NS.A.1. Use this embedded wording as the best available supporting standard description for this workflow.).

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