Free Printable WorksheetMathGrade 8Math Curriculum8.NS.A.2

8.12 Comparing and Ordering Rational and Irrational Numbers Worksheet

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Q: What 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.2 (Primary standard selected for prompt fields: CCSS 8.NS.A.2. Skill statement: Which ordering of the numbers from least to greatest is correct? Associated standards listed with this skill: CCSS 8.NS.A.2; CA 8.NS.A.2; MA 8.NS.A.2. Use this embedded wording as the best available supporting standard description for this workflow.).

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.12 Comparing and Ordering Rational and Irrational Numbers. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.12 Comparing and Ordering Rational and Irrational Numbers - Which ordering of the numbers from least to greatest is correct? (CCSS 8.NS.A.2; CA 8.NS.A.2; MA 8.NS.A.2)

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 8.12 Comparing and Ordering Rational and Irrational Numbers skill assessments:

Problem 1Difficulty: Hard

Order these numbers from least to greatest. Which choice is correct? -sqrt(11), -3.315, -3.317, -3.320, -10/3

A-3.315 < -sqrt(11) < -3.317 < -3.320 < -10/3

B-10/3 < -3.320 < -sqrt(11) < -3.317 < -3.315

C-10/3 < -3.320 < -3.317 < -3.315 < -sqrt(11)

D-10/3 < -3.320 < -3.317 < -sqrt(11) < -3.315

Solution & Explanation:Compare decimal values: -10/3 approx -3.33333, -3.320 = -3.32000, -3.317 = -3.31700, -sqrt(11) approx -3.31662, -3.315 = -3.31500. Because all the numbers are negative, the number with the greater absolute value is smaller. So the order from least to greatest is -10/3 < -3.320 < -3.317 < -sqrt(11) < -3.315.

Problem 2Difficulty: Hard

Which option orders -3.161, -3.163, -3.170, -19/6, -sqrt(10) from least to greatest?

A-3.161 < -sqrt(10) < -3.163 < -19/6 < -3.170

B-3.170 < -19/6 < -sqrt(10) < -3.163 < -3.161

C-3.170 < -19/6 < -3.163 < -sqrt(10) < -3.161

D-3.170 < -19/6 < -3.163 < -3.161 < -sqrt(10)

Solution & Explanation:Place the values on the same number line by using decimal forms: -3.170 = -3.17000, -19/6 approx -3.16667, -3.163 = -3.16300, -sqrt(10) approx -3.16228, -3.161 = -3.16100. Because all the numbers are negative, the number with the greater absolute value is smaller. From least to greatest, the numbers are -3.170 < -19/6 < -3.163 < -sqrt(10) < -3.161.

Problem 3Difficulty: Hard

Choose the correct ordering from least to greatest for -3.150, -3.140, -pi, -22/7, -3.144.

A-3.140 < -pi < -22/7 < -3.144 < -3.150

B-3.150 < -3.144 < -22/7 < -pi < -3.140

C-3.150 < -22/7 < -3.144 < -pi < -3.140

D-3.150 < -3.144 < -pi < -22/7 < -3.140

Solution & Explanation:Estimate the irrational numbers and rewrite any fractions as decimals: -3.150 = -3.1500, -3.144 = -3.1440, -22/7 approx -3.1429, -pi approx -3.1416, -3.140 = -3.1400. Because all the numbers are negative, the number with the greater absolute value is smaller. Therefore the correct ordering is -3.150 < -3.144 < -22/7 < -pi < -3.140.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this 8.12 Comparing and Ordering Rational and Irrational Numbers worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this 8.12 Comparing and Ordering Rational and Irrational Numbers worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice 8.12 Comparing and Ordering Rational and Irrational Numbers online with instant feedback?

Yes! In addition to this printable worksheet, students can practice 8.12 Comparing and Ordering Rational and Irrational Numbers interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

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.2 (Primary standard selected for prompt fields: CCSS 8.NS.A.2. Skill statement: Which ordering of the numbers from least to greatest is correct? Associated standards listed with this skill: CCSS 8.NS.A.2; CA 8.NS.A.2; MA 8.NS.A.2. Use this embedded wording as the best available supporting standard description for this workflow.).