Order & compare large numbers
Theory
To compare large numbers, line them up by place value and look at the first place, from the left, where their digits differ. The symbols \(>\) and \(<\) show which number is larger, and lists can be put in ascending (smallest to largest) or descending (largest to smallest) order.
To compare two whole numbers with the same number of digits, look at the digits one place at a time, starting from the highest place. The first place where the digits differ decides which number is larger.
The symbol \(>\) means greater than and \(<\) means less than. The wide open end always faces the larger number, so \(4\,280\,000 > 4\,208\,000\).
To put numbers in order, compare them in pairs. Ascending order runs from smallest to largest; descending order runs from largest to smallest.
Three symbols are used to compare numbers:
| Symbol | Meaning | Example |
|---|---|---|
| \(>\) | greater than | \(4\,280\,000 > 4\,208\,000\) |
| \(<\) | less than | \(2\,060\,000 < 2\,600\,000\) |
| \(=\) | equal to | \(3\,500\,000 = 3\,500\,000\) |
How to compare or order numbers
- Line up the numbers by place value, ones under ones.
- Scan from the left and stop at the first place where the digits differ.
- Decide which digit is larger there, then place the \(>\), \(<\), or order the list smallest to largest (ascending) or largest to smallest (descending).
They first differ in the ten-thousands place, where \(0 < 8\).
| \(4\,208\,000\) | \(<\) | \(4\,280\,000\) |
All start with \(6\). The hundred-thousands are \(0, 7, 7\). Two have \(7\); their ten-thousands are \(3\) and \(0\), and \(3 > 0\).
Largest is \(6\,730\,000\).
All start with \(5\); sort by the next places.
Ascending: \(5\,028\,000,\ 5\,208\,000,\ 5\,280\,000,\ 5\,802\,000\)
Descending: the same list reversed.
It lies between the two, so it starts \(5\,24\). A \(7\) in the thousands place gives:
\(5\,247\,000\)
Common pitfalls
Frequently asked questions
How do you compare large numbers?
Line the numbers up by place value and compare the digits from the left. The first place where they differ decides which is larger. For example \(3\,542\,000\) and \(3\,524\,000\) first differ in the ten-thousands place, where \(4 > 2\).
What do the > and < symbols mean?
\(>\) means greater than and \(<\) means less than. The wide open end faces the larger number, so \(4\,280\,000 > 4\,208\,000\).
What is ascending and descending order?
Ascending order runs from smallest to largest; descending order runs from largest to smallest. Compare the numbers in pairs by place value to sort them.
How do you know which number is bigger?
With the same number of digits, compare digit by digit from the highest place; the first place that differs tells you. A number with more digits, and no leading zero, is always larger.
Which number is bigger if they start with the same digit?
Keep comparing to the right until the digits differ. \(2\,060\,000\) and \(2\,600\,000\) both start with \(2\), but \(0 < 6\) in the hundred-thousands place, so \(2\,060\,000\) is smaller.