Comparing, Ordering & Rounding

To compare two whole numbers, look at their digits from the left. The first column where they differ decides which is larger. We record the result with $<$ (less than), $>$ (greater than) or $=$ (equal).

Compare $45\,210$ and $45\,120$: the ten-thousands ($4$) and thousands ($5$) match, but in the hundreds column $2 > 1$, so

To order a list, compare them in pairs and line them up smallest-to-largest (ascending) or largest-to-smallest (descending).

Rounding replaces a number with a nearby, tidier one. To round to a given place, look at the digit immediately to its right:

• if that digit is $5$ or more, round up;
• if it is $4$ or less, round down (leave the place as it is).

Worked example. Round $3\,847$ to the nearest hundred. The hundreds digit is $8$; the digit to its right (tens) is $4$, which is less than $5$, so we round down and keep $8$: the answer is $3\,800$.