Worksheets · Pre-Algebra

Classifying real numbers worksheet for Pre-Algebra

The sets nest: every natural number is whole, every whole number is an integer, every integer is rational. The most specific name is the innermost one that fits. A number is irrational when it cannot be written as a fraction of integers, and a square root is rational only when the number under it is a perfect square.

Also taught in Algebra 1, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Classifying Real Numbers

Date Period

Classify each number as asked, using natural, whole, integer, rational, irrational and real.

  1. Name the most specific set

    Which is the most specific set that contains 144?
  2. Which is the most specific set that contains −17?
  3. Which is the most specific set that contains 24?
  4. Which is the most specific set that contains 52?
  5. Which is the most specific set that contains −53?
  6. Which is the most specific set that contains 137?
  7. Which is the most specific set that contains −114?

  1. Classify square roots as rational or irrational

    Is 170 rational or irrational?
  2. Classify 196 as rational or irrational.
  3. Is 169 rational or irrational?
  4. Classify 270 as rational or irrational.
  5. Is 121 rational or irrational?
  6. Classify 256 as rational or irrational.
  7. Is 293 rational or irrational?

  1. Name every set it belongs to

    Name every set that contains −π.
  2. Name every set that contains −2.75.
  3. Name every set that contains 124.
  4. Name every set that contains −0.6‾.
  5. Name every set that contains 10.
  6. Name every set that contains 0.3‾.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Classifying Real NumbersAnswer keyVersion 1

Date Period

Classify each number as asked, using natural, whole, integer, rational, irrational and real.

  1. Name the most specific set

    Which is the most specific set that contains 144?Natural
  2. Which is the most specific set that contains −17?Integer
  3. Which is the most specific set that contains 24?Natural
  4. Which is the most specific set that contains 52?Rational
  5. Which is the most specific set that contains −53?Rational
  6. Which is the most specific set that contains 137?Rational
  7. Which is the most specific set that contains −114?Rational

  1. Classify square roots as rational or irrational

    Is 170 rational or irrational?Irrational
  2. Classify 196 as rational or irrational.Rational, 196=14
  3. Is 169 rational or irrational?Rational, 169=13
  4. Classify 270 as rational or irrational.Irrational
  5. Is 121 rational or irrational?Rational, 121=11
  6. Classify 256 as rational or irrational.Rational, 256=16
  7. Is 293 rational or irrational?Irrational

  1. Name every set it belongs to

    Name every set that contains −π.Irrational, real
  2. Name every set that contains −2.75.Rational, real
  3. Name every set that contains 124.Natural, whole, integer, rational, real
  4. Name every set that contains −0.6‾.Rational, real
  5. Name every set that contains 10.Irrational, real
  6. Name every set that contains 0.3‾.Rational, real

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

−25

  1. The root of 25 is 5, so this is -5.
  2. -5 is an integer, and not whole or natural, because it is negative.

The answer is Integer.

Where students go wrong

Calling every root irrational. The root of 25 is 5, a perfectly good natural number; only roots of non-squares are irrational.

Also called number sets, real number system, classifying numbers or natural whole and integers.

What you can put on this worksheet

The most specific set
Which is the most specific set that contains −4? → Integer
Is the square root rational
Is 74 rational or irrational? → Irrational
Every set it belongs to
Name every set that contains −54. → Rational, real

Questions about these worksheets

Yes. Every classifying real numbers sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Pre-Algebra is usually taken around 7th or 8th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the classifying real numbers questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: the most specific set, is the square root rational and every set it belongs to. Tick as many as you want and set how many of each, or let it spread them evenly.

Calling every root irrational. The root of 25 is 5, a perfectly good natural number; only roots of non-squares are irrational.