Comparing and ordering numbers up to a million

When we compare numbers, we look at which one is bigger and which is smaller. We use three signs: $<$ (less than), $>$ (greater than) and $=$ (equal to).

Start with the highest place

The simplest trick: compare the digits from left to right. Start with the leftmost place — the largest one.

285 472 vs. 198 999

Hundred-thousands: 2 vs. 1. 2 > 1, so 285 472 > 198 999. You don't even have to look at the other digits.

When the leftmost digits match, move one step to the right:

4 280 vs. 4 175

Thousands match (both 4). Look at hundreds: 2 vs. 1. 2 > 1, so 4 280 > 4 175.

And if hundreds match too? Carry on through tens and then ones.

6 753 vs. 6 758

Thousands 6 = 6, hundreds 7 = 7, tens 5 = 5. The ones finally split them: 3 < 8, so 6 753 < 6 758.

Numbers with the same length

When two numbers have the same number of digits (both six-digit, say) you simply walk through them place by place from the left.

The first difference is in ten-thousands: 8 > 7. So 285 472 > 274 999. The rest of the digits don't matter.

Different lengths

A four-digit number is always smaller than a five-digit number, which is always smaller than a six-digit number, and so on. Count the digits first.

999 < 1 000 < 9 999 < 10 000 < 999 999 < 1 000 000

If the lengths differ, the longer one wins. Easy.

Ordering a list

Take a list and break it into groups by their highest place. Then order within each group.

4 280, 152 030, 4 175, 39 008

By number of digits:

• four-digit: 4 280 and 4 175 (within group: 4 175 < 4 280)
• five-digit: 39 008
• six-digit: 152 030

Final order from smallest to largest:

4 175 < 4 280 < 39 008 < 152 030

What's next

• Rounding large numbers
• For parents
• Back to the introduction

Try it out

• ⚖️ Compare numbers — pick the right sign
• 🔀 Order numbers — smallest to largest