Lesson 2: Fractions and Decimals on the Number Line

Property

To plot a fraction with a denominator of 10 or 100 on a number line, divide the segment between each whole number (e.g., 0 to 1, 1 to 2) into 10 or 100 equal intervals. The numerator indicates how many intervals to count from the starting whole number. For a mixed number $A \frac{b}{c}$, start at the whole number $A$ and count $b$ intervals.

Examples

• To locate $\frac{7}{10}$ on a number line, divide the space between 0 and 1 into 10 equal parts and place a point on the 7th mark.
• To locate $\frac{35}{100}$ on a number line, divide the space between 0 and 1 into 100 equal parts and place a point on the 35th mark.
• To locate $2 \frac{4}{10}$ on a number line, start at the whole number 2, and then move 4 tenths of the way towards 3.

Explanation

Fractions with denominators of 10 or 100 are special because they directly correspond to decimal place values. To plot these fractions, you can think of the number line as a ruler divided into tenths or hundredths. The numerator tells you exactly how many of these small tick marks to count. For mixed numbers, locate the whole number first, and then use the numerator to count the fractional parts from there.

Property

To locate a decimal on a number line, first identify the whole numbers the decimal is between. Then, divide the space between these whole numbers into ten equal parts, representing tenths. For hundredths, imagine each tenth is further divided into ten smaller parts.

Examples

• To locate $0.4$, find the fourth mark on a number line divided into tenths between $0$ and $1$.
• To locate $1.6$, find the sixth mark on a number line divided into tenths between $1$ and $2$.
• To locate $0.83$, find the eighth tenth ($0.8$), then move three hundredths past it, placing the point slightly before the ninth tenth ($0.9$).

Explanation

Locating a decimal on a number line is similar to finding a fraction. The number line is based on powers of ten. The space between each whole number is divided into ten equal parts to show tenths. Each of those tenths can be subdivided into another ten parts to show hundredths, allowing for precise placement of decimal values.

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.