Is Zero a Positive or Negative Integer? Here’s the Surprising Answer

PDF download Download Article
Learn how zero fits into the number line—including whether its positive, negative, an integer, whole number, or a combo of these
PDF download Download Article

If you’re taking a math class, you’ll definitely encounter integers, as well as positive and negative numbers. But where does 0 fall within these categories? Is it positive or negative? Is it an integer or not? If these questions have you scratching your head, you’re not alone. 0 is an oddball in math, and categorizing it requires some extra thinking and creativity. This guide will help you understand exactly how 0 fits in with respect to positive and negative integers. Keep reading for a crystal clear explanation, plus a few examples to really bring these ideas home.

Things You Should Know

  • Zero is an integer, but it’s neither positive nor negative. It’s the only number that’s not positive or negative.
  • Zero is neither greater than zero nor less than zero. Therefore, by this definition, it’s neither positive nor negative.
  • Zero is still an integer because it’s a whole number and doesn’t contain any fractional part. This means it contains no fractions or decimals.
  • A positive integer is a whole number greater than zero, while a negative integer is a whole number less than zero.
Section 1 of 3:

Is zero a positive or negative integer?

PDF download Download Article
  1. On a traditional number line, zero sits in the middle between the positive and negative numbers. By definition, negative numbers are less than zero and located to the left of zero on a number line, while positive numbers are greater than zero and located to the right. Since zero doesn’t fit these definitions, it’s not considered positive or negative. [1]
    • Zero is the only number that isn’t positive or negative.
    2. Advertisement
Section 2 of 3:

Why is 0 an integer?

PDF download Download Article
  1. A “whole” number is any number that has no fractional parts. In other words, it doesn’t contain fractions or decimals. An integer can be positive, negative, or 0, but it cannot have fractional parts.
    • For example, the numbers -14, -1, 0, 7, 21, and 37 are all integers because they are whole numbers.
    • The numbers -2.7, -½, 15.1, and π are not integers because they contain fractional parts (either as fractions or decimals).
Section 3 of 3:

Proof that Zero Can’t be Positive or Negative

PDF download Download Article
  1. Let’s use the example -2 x 0 = 0, assuming zero is positive. We know that -2 is a negative number. We also know that if we multiply a negative number by a positive number, the answer will always be negative. [2] Therefore, if we assume 0 is positive, then -2 x 0 should give us a negative answer. But the answer is 0, which we said was positive. This is a contradiction, which means our original assumption was incorrect. [3]
    • Since a number can’t be positive and negative at the same time, we must assume that 0 is neither positive nor negative.
  2. Let’s try -2 x 0 = 0 again, assuming zero is negative this time. We know that -2 is a negative number. We also know that if we multiply a negative number by another negative number, the answer will always be positive. [4] Therefore, if we assume 0 is negative, then -2 x 0 should give us a positive answer. But the answer is 0, which we assumed was negative. Once again, we have a contradiction. This proves that our original assumption was wrong. [5]
    • A number can’t be negative and positive at the same time. Therefore, 0 is neither positive nor negative.
    3. Advertisement

Community Q&A

Search
Add New Question
  • Question
    Why is 0 times x equals to 0?
    Community Answer
    The reason this is true is that, according to the "zero property of multiplication," anything multiplied by zero equals zero.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 4 Helpful 3
  • Question
    Why can't 0 be both positive and negative?
    Community Answer
    In one sense, that is a meaningless and inconceivable condition. In another sense, however, it could be considered true: zero is "more positive" than negative numbers and at the same time "more negative" than positive numbers. (This is a rather trivial notion, however, in that something similar could be said of any number.)
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 1 Helpful 4
  • Question
    What is the absolute value of negative zero?
    I_l1ke_gam3s
    Community Answer
    There is no such thing as “negative zero”. Zero is neither positive nor negative. Zero is just zero, with an absolute value of zero.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 4 Helpful 2
See more answers
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
      Advertisement

      Video

      Tips

      Submit a Tip
      All tip submissions are carefully reviewed before being published
      Name
      Please provide your name and last initial
      Submit
      Thanks for submitting a tip for review!

      You Might Also Like

      How to
      Use an Abacus
      How to
      Calculate Percentages
      The Trachtenberg Method: Learn to Calculate Multi-Digit Numbers Quickly
      How to
      Measure Centimeters
      How to
      Calculate Ratios
      How to
      Use the Percent Change Formula
      How to
      Find the Y Intercept
      How to
      Calculate Percentage Increase
      How to
      Calculate Percentages on a Calculator
      How to
      Write Numbers in Words
      How to
      Find the Domain of a Function
      How to
      Measure Grams
      How to
      Calculate Pi
      How to
      Calculate Growth Rate
      Advertisement

      References

      1. ↑ https://mathworld.wolfram.com/Zero.html
      2. ↑ https://web.gccaz.edu/~johwd63181/MAT115/chapter1/text/Section%201.3.pdf
      3. ↑ https://www.ma.imperial.ac.uk/~buzzard/maths/teaching/18Aut/M1F/solns03.pdf
      4. ↑ https://web.gccaz.edu/~johwd63181/MAT115/chapter1/text/Section%201.3.pdf
      5. ↑ https://www.ma.imperial.ac.uk/~buzzard/maths/teaching/18Aut/M1F/solns03.pdf

      About This Article

      Thanks to all authors for creating a page that has been read 83,083 times.

      Did this article help you?

      Advertisement