Order & compare numbers
Theory
Comparing and ordering numbers is a Year 3 place value skill: deciding which whole number is larger or smaller by comparing the digits from the left, using the greater than and less than symbols, and putting numbers in ascending or descending order. This Year 3 maths page explains how to compare place by place, number lines, making the largest and smallest numbers from digits, halfway numbers and rounding to compare sizes. Curriculum: VC2M3N02 / AC9M3N01.
To compare two numbers is to decide which is larger, which is smaller, or whether they are equal. To order numbers is to line them up in a row: ascending order means smallest to largest, and descending order means largest to smallest. Years can be ordered too: the earliest year is the smallest number.
Compare numbers using the symbols \(<\) for is less than, \(>\) for is greater than, and \(=\) for is equal to. The pointy end always points at the smaller number, so \(2319 < 2391\).
First count the digits: a whole number with more digits is always larger, so \(9999 < 10\,000\). When two numbers have the same number of digits, compare them digit by digit from the left. The first place where the digits differ decides which number is bigger.
The halfway number between two numbers sits exactly in the middle: halfway between \(6000\) and \(7000\) is \(6500\). Rounding swaps a number for the nearest tidy number, which helps you say roughly how big it is.
These facts help you compare and order whole numbers quickly.
| Symbol | Meaning | Example |
|---|---|---|
| \(<\) | is less than | \(2319 < 2391\) |
| \(>\) | is greater than | \(6802 > 6280\) |
| \(=\) | is equal to | \(620 = 620\) |
How to compare or order whole numbers
- Count the digits. A number with more digits is larger. If the digit counts are different, you already know which is bigger.
- Line up the places. If the numbers have the same number of digits, compare from the left: ten thousands, then thousands, then hundreds, then tens, then ones.
- Decide and explain. The first place where the digits differ tells you which number is larger. Say which place decided it.
- Order a list. Pick the smallest each time (ascending) or the largest each time (descending) until every number has a spot.
How to find which number is closest
- Find each difference. Work out how far each number is from the target.
- Pick the smallest difference. That number is the closest.
| \(\text{thousands, hundreds}\) | \(:\) | \(5 = 5,\ 2 = 2\) |
| \(\text{tens}\) | \(:\) | \(0 < 8\) |
| \(5208\) | \(<\) | \(5280\) |
The symbol is \(<\).
| \(\text{thousands}\) | \(:\) | \(\text{all } 3\) |
| \(\text{hundreds}\) | \(:\) | \(4,\ 4,\ 0,\ 0\) |
| \(3048\) | \(<\) | \(3084 < 3408 < 3480\) |
In order: \(3048,\ 3084,\ 3408,\ 3480\).
| \(\text{each mark}\) | \(=\) | \(10\) |
| \(600 + 70\) | \(=\) | \(670\) |
The arrow points to \(670\).
| \(\text{thousands}\) | \(:\) | \(16\,025\text{ has } 16\) |
| \(\text{hundreds}\) | \(:\) | \(6,\ 2,\ 6\) |
| \(15\,620\text{ vs }15\,602\) | \(:\) | \(2\text{ tens} > 0\text{ tens}\) |
Descending: \(16\,025,\ 15\,620,\ 15\,602,\ 15\,260\).
(i) What is the largest number?
(ii) What is the smallest four-digit number?
(iii) What is the second largest number?
| \(\text{largest}\) | \(:\) | \(9640\) |
| \(\text{smallest}\) | \(:\) | \(4069\) |
| \(\text{second largest}\) | \(:\) | \(9604\) |
(i) \(9640\).
(ii) \(4069\): 0 cannot go first, so 4 leads.
(iii) \(9604\): swap the last two digits of the largest.
(ii) Round \(6450\) to the nearest thousand.
(iii) Round \(36\,900\) to the nearest ten thousand.
| \(7000 + 500\) | \(=\) | \(7500\) |
| \(6450\) | \(\to\) | \(6000\ (4 \text{ hundreds})\) |
| \(36\,900\) | \(\to\) | \(40\,000\ (6 \text{ thousands})\) |
(i) \(7500\).
(ii) \(6000\): the hundreds digit is 4, so round down.
(iii) \(40\,000\): the thousands digit is 6, so round up.
| \(2008 - 2000\) | \(=\) | \(8\) |
| \(2080 - 2000\) | \(=\) | \(80\) |
| \(2180 - 2000\) | \(=\) | \(180\) |
\(2008\) is only 8 away, so it is closest to \(2000\). (\(2800\) is 800 away.)
Common pitfalls
Frequently asked questions
How do you compare two numbers?
First count the digits. A number with more digits is larger. If they have the same number of digits, compare digit by digit from the left. The first place where the digits differ decides which number is bigger.
What do the greater than and less than symbols mean?
The symbol \(<\) means "is less than" and \(>\) means "is greater than". The pointy end always points at the smaller number.
What does ascending and descending order mean?
Ascending order means smallest to largest. Descending order means largest to smallest. For example, \(357,\ 375,\ 537\) is ascending and \(537,\ 375,\ 357\) is descending.
Is a number with more digits always bigger?
Yes. For whole numbers, a number with more digits is always larger. For example, \(9999\) has four digits and \(10\,000\) has five digits, so \(9999 < 10\,000\).
How do you make the largest number from a set of digits?
Put the biggest digit in the highest place and order the digits from largest to smallest. Using \(3,\ 8,\ 1\) and \(5\), the largest number is \(8531\).
How do you find the number halfway between two numbers?
Find the middle. Halfway between \(3000\) and \(4000\) is \(3500\), because it is 500 from each end.
How do you put years in order?
Years are numbers, so compare them like any other numbers. The earliest year is the smallest: \(1975,\ 1988,\ 2001\) is from earliest to latest.