1/3 → 0.3̄
Every fraction is secretly a division problem. Today we'll turn one third into a decimal.
Here's our fraction — one third. The bar between numerator and denominator means 'divide.'
So we'll divide one by three using the long-division house.
Three doesn't fit into one. Write zero on top, then add a decimal point and zeros so we can keep dividing.
How many threes fit into ten? Three! Write three above the first zero.
After subtracting we have one left, bring down a zero — that's ten again. So another three.
And again — three. Notice anything?
The threes will keep coming forever. The decimal never ends — it repeats.
Mathematicians draw a tiny bar over the digit that repeats. That's bar notation.
One third equals zero point three, repeating — a repeating decimal.