Question

Factor Word Problem?

Answer 1

`1 = 0.9999....`

Explanation:

`1/3 = 0.3333...`

`1 = 3/3 = 3 * 1/3`

`1/3 * 3 = 0.3333... * 3`

`0.333.. * 3 = 0.9999...`

`1 = 0.9999....`

`0.3333..` is the decimal notation for `1/3`. the `3` in `0.3333...` is recurring.

`1` is `1/3 * 3`.

since `0.3333..` is the decimal notation for `1/3`, `0.3333...` can be multiplied by `3` to find `1` in decimal notation.

`0.3333...` mulltiplied by `3` is `0.9999....`

with more `9`s in `0.9999...`, it gets closer and closer to `1`.
when the `9`s in `0.9999...` are infinite, the number is said to equal `1`.

this makes `0.999...` suitable repeating decimal notation for `1`.