Place Value & Ordering (Years 6–8) — Maths

Look at a supermarket receipt, a football score, or the odometer in a car: every number you meet is built from just ten digits (0–9). The clever part is place value — the same digit is worth a different amount depending on where it sits. The 5 in £5 buys a sandwich; the 5 in £500 buys a laptop. Same digit, very different money.

Why this matters: place value is the foundation of every other number skill — adding, rounding, comparing prices, reading a bank balance. Get a digit in the wrong column and £50 becomes £500. Almost every "silly" arithmetic slip is really a place-value slip.

4732 = 4 thousands + 7 hundreds + 3 tens + 2 units

Reading the columns

Think of the columns as boxes lined up in a row. Starting from the right, each box is worth ten times the one before it — units, then tens, then hundreds, then thousands, and on it goes.

Thousands	Hundreds	Tens	Units
4	7	3	2
4000	700	30	2

So 4732 means 4 thousands + 7 hundreds + 3 tens + 2 units, which is 4000 + 700 + 30 + 2.

The digit 7 in 4732 isn't just "7" — it sits in the hundreds column, so it's worth 700. The very same 7 in 4372 would be worth only 70. Position is everything.

Why position matters: the 2 in 20 and the 2 in 200 are the same digit, but each step left makes it worth ten times more. Move a digit one column left → ×10; one column right → ÷10. This is exactly why adding a zero on the end of a whole number makes it ten times bigger.

Decimals — going past the units

In 3.06 the 0 holds the tenths place so the 6 stays in the hundredths.

What if we need part of one? The decimal point is the fence between whole amounts on the left and parts of one on the right. The columns keep dividing by ten as you cross it:

Units	•	Tenths	Hundredths	Thousandths
3	•	0	6	0

So in 3.06 the 6 is in the hundredths column → six hundredths (0.06). The 0 in the tenths column isn't lazy — it holds the 6 in the right place, just like £3.06 is not the same as £3.60.

Comparing & ordering numbers

0.7 sits to the right of 0.65 on the line, so 0.7 > 0.65 — more digits does not mean bigger.

To put numbers in order, treat it like judging a race photo — line everything up fairly first, then look for the first place they differ:

Line the numbers up by their decimal point.
Compare digits from the left — the first column where they differ decides which is bigger.
If one decimal is shorter, add zeros on the end to make them the same length (0.4 = 0.40).

Which is bigger, 0.7 or 0.65? Write 0.7 as 0.70 so both have two decimal places. Compare tenths: 7 vs 6 → 0.70 wins straight away. So 0.7 > 0.65.

Common mistake: a decimal with more digits is not automatically bigger. 0.65 has more digits than 0.7 but is smaller — always compare column by column, never by counting digits.

Rounding to a nearby number

8649 falls just before halfway (8650), so to the nearest hundred it rounds down to 8600.

Rounding means swapping a number for a tidy nearby one. Look at the digit just after the place you are rounding to: 5 or more rounds up, 4 or less stays. So 47,380 to the nearest thousand is 47,000 (the hundreds digit is 3, so round down), while 8,649 to the nearest hundred is 8,600.

The < and > symbols

< means "less than" and > means "greater than". The wide open end always faces the bigger number — picture a hungry mouth that always wants the larger amount: 3 < 8 and 8 > 3.

Memory hook: a digit's value = its face value × its column. To compare, line up the decimal points and read left to right — the greedy mouth points at the bigger number.