Zero

High School

Definition

A number that expresses something that has no size, quantity, or magnitude. If you see that something has the value of zero, it essentially means there is no amount. It is represented with the figure 0. It is regarded as being neither positive or negative.

Worked examples

\(5 - 5 = 0\)

When you subtract a number from itself, the result is zero — no quantity remains.

\(7 \times 0 = 0\)

Any number multiplied by zero gives zero — there are zero groups of that number.

\(0 + 8 = 8 \quad 0 \times 12 = 0 \quad \frac{0}{3} = 0\)

Zero is the additive identity; multiplying or dividing zero behaves specially.

Common mistakes

\(\frac{5}{0} = 0\) → \(\frac{5}{0}\) is undefined Division by zero has no meaning in mathematics — you cannot divide by zero.
\(0\) is a positive number → \(0\) is neither positive nor negative Zero sits at the center of the number line and has no sign.
\(\frac{0}{0} = 1\) because anything divided by itself is 1 → \(\frac{0}{0}\) is undefined (indeterminate) Even zero divided by zero has no single well-defined value.

Where you'll use it next

Zero is foundational in algebra for solving equations, defining the origin on coordinate planes, working with polynomials and their roots, and understanding limits and calculus.

Found in 1 StudyPug lesson

Subtracting with the number zero

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