Question

What is 1.5 repeated as a fraction?

Answer 1

`1.5555... = 1.bar5 = 14/9`

Explanation:

There are a couple ways to turn a repeating decimal into a fraction. Here's the mathematical way to derive it:

Our number is a whole (1) plus a decimal portion (0.55555...). We will turn this decimal portion into a proper fraction and then add our whole (1) back to it.

Let `x = 0.55555...`

Multiply both sides by 10.

`10x = 5.55555...`

Subtract the new whole portion (5) from both sides.

`10x - 5 = 0.55555...`

Notice our new right-hand side is exactly what we called `x` earlier. We replace it with `x` to get:

`10x - 5 = x`

Solving for `x`:

`9x = 5`

`color(white)1 x = 5/9`

So our original number 1.55555... is equal to `1 + 5/9`, which is `14/9`.