Place Value & Rounding

In our number system the position of a digit decides its value. Reading from the right, the columns are units, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions.

In $452\,617$ the digit $5$ sits in the ten-thousands column, so it is worth $50\,000$ — not $5$. The very same digit can mean very different amounts depending on where it stands.

Rounding replaces a number with a nearby, tidier one. To round to a given place, look at the digit just to the right: if it is $5$ or more, round up; if it is $4$ or less, round down.

Worked example. Round $348\,675$ to the nearest thousand. The digit to the right of the thousands column is $6$ (a hundreds digit), and $6 \geq 5$, so round up: $348\,675 \approx 349\,000$.