Equivalent Fractions and Decimals on the Number Line

Property A single point on the number line can be represented by both a fraction and a decimal. If a fraction and a decimal have the same value, they are located at the exact same point. For example, $\frac{1}{2} = 0.5$.

Examples The point halfway between $0$ and $1$ can be labeled as both $\frac{1}{2}$ and $0.5$. On a number line divided into ten equal parts between $0$ and $1$, the fourth mark represents both $\frac{4}{10}$ and $0.4$. The fraction $\frac{3}{4}$ and the decimal $0.75$ name the same point, which is located three quarters of the way from $0$ to $1$.

Explanation Fractions and decimals are two different ways to write numbers that are not whole numbers. Since they can represent the same value, they will occupy the same position on a number line. Understanding this equivalence is key to seeing the relationship between fractions and decimals. This means a single point can have multiple labels, such as a fraction and its equivalent decimal form.