1/3 as a decimal
How do we write a fraction like one-third as a decimal? Let's find out using long division.
We set up one divided by three using the long-division house.
Three doesn't fit into one, so we put a zero on top and add a decimal point.
Then we add zeros after the decimal so we can keep on dividing.
How many threes fit in ten? Three of them. Write three in the tenths place.
Three times three is nine. Ten minus nine leaves a remainder of one.
Bring down the next zero. We have ten again — exactly what we just had.
So three fits in three more times. We write another three on top.
Three times three is nine again. Ten minus nine is one — again.
Notice the pattern: the same remainder, the same digit, every single time. It will never stop.
We draw a bar over the three to mean 'this digit repeats forever.'
One-third is a repeating decimal. Every rational number's decimal either ends or eventually repeats.
One-third equals zero point three repeating. Predictable, every time.