Locating Decimals on the Number Line

Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.

Example

Locate \(0.4\) on a number line.

Solution

The decimal \(0.4\) is equivalent to \(\frac{4}{10},\) so \(0.4\) is located between \(0\) and \(1.\) On a number line, divide the interval between \(0\) and \(1\) into \(10\) equal parts and place marks to separate the parts.

Label the marks \(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0.\) We write \(0\) as \(0.0\) and \(1\) as \(1.0,\) so that the numbers are consistently in tenths. Finally, mark \(0.4\) on the number line.

A number line is shown with 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 labeled. There is a red dot at 0.4.

Example

Locate \(-0.74\) on a number line.

Solution

The decimal \(-0.74\) is equivalent to \(-\frac{74}{100},\) so it is located between \(0\) and \(-1.\) On a number line, mark off and label the multiples of \(-0.10\) in the interval between \(0\) and \(-1\) (\(-0.10\), \(-0.20\), etc.) and mark \(-0.74\) between \(-0.70\) and \(-0.80,\) a little closer to \(-0.70\).

A number line is shown with negative 1.00, negative 0.90, negative 0.80, negative 0.70, negative 0.60, negative 0.50, negative 0.40, negative 0.30, negative 0.20, negative 0.10, and 0.00 labeled. There is a red dot between negative 0.80 and negative 0.70 labeled as negative 0.74.

Optional Video: Identify Decimals on the Number Line

This lesson is part of:

Introducing Decimals

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