Numbers up to 10,000 - Rounding Numbers to the nearest 10

Rounding means making a number simpler but keeping its value close to the original number. When we round to the nearest $10$, we are looking for the multiple of $10$ (numbers like $10, 20, 30, ...$) that is closest to our number.

To round to the nearest $10$, always look at the digit in the ones place. Imagine a 'Rounding Hill' where numbers ending in $0, 1, 2, 3,$ and $4$ are on the left slope and roll back down, while numbers ending in $5, 6, 7, 8,$ and $9$ are on the peak or right slope and roll forward to the next ten.

If the digit in the ones place is less than $5$ (specifically $0, 1, 2, 3,$ or $4$), we round down. This means the tens digit stays the same, and the ones digit becomes $0$. Visually, on a number line, the number is closer to the smaller ten.

If the digit in the ones place is $5$ or greater ($5, 6, 7, 8,$ or $9$), we round up. This means we increase the tens digit by $1$ and change the ones digit to $0$. Even though $5$ is exactly in the middle, the standard rule is to always round up.

When rounding numbers up to $10,000$ to the nearest $10$, the hundreds and thousands digits usually remain unchanged. For example, in the number $4,562$, we only focus on the 'tens' and 'ones' part ($62$) to decide how to round.

In special cases where the tens digit is a $9$ and we need to round up (e.g., $1,298$), the $9$ becomes a $10$. This means the $0$ stays in the tens place and $1$ is carried over to the hundreds place, making the result $1,300$.

On a visual number line divided into intervals of $10$, rounding helps you identify which 'station' the number is closest to. For example, $87$ is located between $80$ and $90$, but it sits much closer to $90$.