Place value: compare and order numbers

The idea

The value of a digit depends on where it sits. In 48,350 the 4 is worth 40,000 and the 8 is worth 8,000; in 48,305 the digits look similar but the numbers are different.

To compare two numbers with the same number of digits, work from the left, comparing one place at a time. Keep going until you find a place where the digits differ — that place decides which number is bigger, and nothing to the right of it matters.

To order a set of numbers, compare them in the same way, or sort by the highest place first and refine. Writing numbers in a place-value grid (ten-thousands, thousands, hundreds, tens, ones) makes the comparison visual.

Worked example

Which is greater: 48,305 or 48,350?

1. Both numbers have 5 digits, so compare from the left.
2. Ten-thousands: 4 and 4 — the same. Thousands: 8 and 8 — the same. Hundreds: 3 and 3 — the same.
3. Tens: 0 in 48,305 but 5 in 48,350 — this is the first difference.
4. 5 tens is more than 0 tens, so 48,350 is greater.

Answer: 48,350

Watch out

• Comparing from the right (the ones end) — always start from the left.
• Thinking a number with more digits after a shared start must be bigger when the deciding digit says otherwise.
• Misreading 306,040 as 'thirty-six thousand' — group digits in threes from the right.