Number System - Rounding Off Numbers

Rounding is the mathematical process of simplifying a number while keeping its value close to the original. For example, if you have $47$ stickers, you can say you have 'about $50$'. On a horizontal number line, $47$ is physically closer to the point $50$ than to $40$.

To round to the nearest $10$, we observe the digit in the ones place. If this digit is $5, 6, 7, 8,$ or $9$, we 'round up' by adding $1$ to the tens digit and changing the ones digit to $0$. If it is $4, 3, 2, 1,$ or $0$, we 'round down' by keeping the tens digit the same and changing the ones digit to $0$.

To round to the nearest $100$, we focus on the tens digit. If the tens digit is $5$ or more, we increase the hundreds digit by $1$. If the tens digit is less than $5$, the hundreds digit stays the same. All digits to the right (tens and ones) are replaced with $0$. Think of it as finding which 'century' number (like $200$ or $300$) our number is closest to on a scale.

To round to the nearest $1000$, we look at the hundreds digit. If the hundreds digit is $\ge 5$, add $1$ to the thousands digit. If the hundreds digit is $< 5$, the thousands digit remains unchanged. The hundreds, tens, and ones places are all set to $0$.

The 'Midpoint Rule' states that when a number is exactly halfway between two targets (ending in $5, 50, 500,$ etc.), we always round up to the higher value. For instance, the number $15$ is exactly in the middle of $10$ and $20$, so we round it up to $20$.

When rounding large numbers like Ten Thousands or Lakhs, always identify the 'rounding digit' and the 'neighbor digit' to its immediate right. Only the neighbor digit determines whether to round up or stay the same, regardless of how large the digits further to the right are.