Common fractions and decimals

${\displaystyle \frac{1}{2}}=0.5$‍

Help me see how these are equal.

There are three ways we can think about this.

Way 1: Using fractions

Let's convert ${\displaystyle \frac{1}{2}}$‍ to a fraction out of $10$‍:

$\phantom{=}{\displaystyle \frac{1}{2}}$‍

$={\displaystyle \frac{1\times 5}{2\times 5}}\text{Multiplied the top and bottom by 5.}$‍

$={\displaystyle \frac{5}{10}}$‍

$=0.5$‍

Way 2: Using area

Let's show ${\displaystyle \frac{1}{2}}$‍ by shading in $1$‍ out of $2$‍ parts:

Let's show $0.5$‍ by shading in $5$‍ out of $10$‍ parts:

These two areas are equal! So, ${\displaystyle \frac{1}{2}}$‍ and $0.5$‍ are equal:

Way 3: Using number lines

Let's plot ${\displaystyle \frac{1}{2}}$‍ on a number line:

Let's also plot $0.5$‍ on a number line:

${\displaystyle \frac{1}{2}}$‍ and $0.5$‍ must be equal because they are at the same spot on the number lines.

${\displaystyle \frac{1}{4}}=0.25$‍

Help me see how these are equal.

There are two ways we can think about this.

Way 1: Using fractions

Let's convert ${\displaystyle \frac{1}{4}}$‍ to a fraction out of $100$‍:

$\phantom{=}{\displaystyle \frac{1}{4}}$‍

$={\displaystyle \frac{1\times 25}{4\times 25}}\text{Multiplied the top and bottom by 25.}$‍

$={\displaystyle \frac{25}{100}}$‍

$=0.25$‍

Way 2: Using number lines

Let's plot ${\displaystyle \frac{1}{4}}$‍ on a number line:

Let's also plot $0.25$‍ on a number line:

${\displaystyle \frac{1}{4}}$‍ and $0.25$‍ must be equal because they are at the same spot on the number lines.

${\displaystyle \frac{1}{5}}=0.2$‍

Help me see how these are equal.

There are three ways we can think about this.

Way 1: Using fractions

Let's convert ${\displaystyle \frac{1}{5}}$‍ to a fraction out of $10$‍:

$\phantom{=}{\displaystyle \frac{1}{5}}$‍

$={\displaystyle \frac{1\times 2}{5\times 2}}\text{Multiplied the top and bottom by 2.}$‍

$={\displaystyle \frac{2}{10}}$‍

$=0.2$‍

Way 2: Using area

Let's show ${\displaystyle \frac{1}{5}}$‍ by shading in $1$‍ out of $5$‍ parts:

Let's show $0.2$‍ by shading in $2$‍ out of $10$‍ parts:

These two areas are equal! So, ${\displaystyle \frac{1}{5}}$‍ and $0.2$‍ are equal:

Way 3: Using number lines

Let's plot ${\displaystyle \frac{1}{5}}$‍ on a number line:

Let's also plot $0.2$‍ on a number line:

${\displaystyle \frac{1}{5}}$‍ and $0.2$‍ must be equal because they are at the same spot on the number lines.

Practice 1: Converting from fractions to decimals

Practice 2: Converting from decimals to fractions