---
title: "8.NR.1: Irrational Numbers Overview (Georgia Mathematics standard)"
code: 8.NR.1
cite_as: Georgia Standards of Excellence, Mathematics, 8.NR.1
subject: math
grades:
  - grade-8
language: en
canonical_url: https://georgiahomeroom.org/standards/code/8.NR.1
md_url: https://georgiahomeroom.org/standards/code/8.NR.1.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/8.NR.1.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/grade-8.md
index: https://georgiahomeroom.org/standards/index.md
---

# 8.NR.1: Irrational Numbers Overview

Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications.

- Subject: Mathematics
- Appears in: Grade 8, https://georgiahomeroom.org/standards/math/grade-8.md

## Expectations

- **8.NR.1.1**: Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.
- **8.NR.1.2**: Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.

## Georgia Milestones coverage

- Mathematics Grade 8 (EOG). Numerical Reasoning. Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications. (about 19% of the test; 11 points; shared with other standards, so count these points once and never add them up per standard)

## What mastery looks like

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

- **Beginning**: Recognize irrational numbers as a category distinct from rational numbers. Identify whole-number values between which an irrational number belongs.
- **Developing**: Classify real numbers as rational or irrational. Approximate irrational numbers by estimating or locating them on a number line.
- **Proficient**: Convert a decimal expansion that repeats into a rational number. Compare an irrational number to another number (rational or irrational) by using a benchmark or number line. Estimate the values of expressions that contain both rational and irrational numbers.
- **Distinguished**: Solve realistic problems involving rational approximations of irrational numbers, including using estimation.

## The same standard across grades

- Kindergarten, K.NR.1: Demonstrate and explain the relationship between numbers and quantities up to 20; connect counting to cardinality (the last number counted represents the total quantity in a set). https://georgiahomeroom.org/standards/code/K.NR.1.md
- Grade 1, 1.NR.1: Extend the count sequence to 120. Read, write, and represent numerical values to 120 and compare numerical values to 100. https://georgiahomeroom.org/standards/code/1.NR.1.md
- Grade 2, 2.NR.1: Using the place value structure, explore the count sequences to represent, read, write, and compare numerical values to 1000 and describe basic place-value relationships and structures. https://georgiahomeroom.org/standards/code/2.NR.1.md
- Grade 3, 3.NR.1: Use place value reasoning to represent, read, write, and compare numerical values up to 10,000 and round whole numbers up to 1,000. https://georgiahomeroom.org/standards/code/3.NR.1.md
- Grade 4, 4.NR.1: Recognize patterns within the base ten place value system with quantities presented in real-life situations to compare and round multi-digit whole numbers through the hundred-thousands place and compare decimal numbers to the hundredths place. https://georgiahomeroom.org/standards/code/4.NR.1.md
- Grade 5, 5.NR.1: Use place value understanding to solve real-life, mathematical problems. https://georgiahomeroom.org/standards/code/5.NR.1.md
- Grade 6, 6.NR.1: Solve relevant, mathematical problems involving operations with whole numbers, fractions, and decimal numbers. https://georgiahomeroom.org/standards/code/6.NR.1.md
- Grade 7, 7.NR.1: Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers). https://georgiahomeroom.org/standards/code/7.NR.1.md
- **Grade 8, 8.NR.1 (this standard)**: Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.