Question

But how does 0.2 convert to 1/5?

Answer 1

`0.2=2/10=1/5`

Explanation:

`0.2` is two-tenths, which is `2/10`. Reduce `2/10` to `1/5`.

Answer 2

`0.2=2/10=1/5`

Explanation:

To convert from decimals to fractions, divide numbers in the tenths place (e.g. 0.7) by ten, numbers in the hundredths place (e.g. 0.45, 0.03, etc.) by one hundred, and so on. A more "mathematical" approach is to multiply the decimal by a power of ten for every number after the decimal (e.g. `0.45 *100 = 45`), divide by that power of ten (e.g. `45/100`), then reduce (`45/100=9/20`). For 0.2, the tenths place, 2, is divided by 10: `2/10`, which reduces to `1/5` (alternatively, `(0.2*10)/10=2/10=1/5`).

To convert from fractions to decimals, use division. For `1/5`, divide 1 by 5 (demonstrating long division is kind of difficult on Socratic, however) which equals 0.2. (Other examples: `3/7 = 0.4286`, `9/8 = 1.125`)