0.45 is smaller than 0.5: place value
The Short Answer
Place value asks what a digit is worth because of where it sits. Every column is ten times the one to its right, in both directions, and that single fact answers most of these questions. The trap is decimals: 0.45 has more digits than 0.5 and is smaller, because the first digit after the point is what decides.
What is a place value question?
Place value is what a digit is worth because of where it sits. The 8 in 2 480 619 is worth eighty thousand; the same 8 in 618 is worth eight.
It is one of the first things the 11+ tests and one of the easiest places to lose a mark, because the method feels too simple to need doing carefully.
Here is the idea the whole topic hangs on, and it is worth saying at the kitchen table: 0.45 is smaller than 0.5.
The frame goes further
Your child already knows how a place value frame works. At this level it simply stretches: millions, hundreds of thousands, tens of thousands, thousands, and then the hundreds, tens and units they have had for years.
The rule has not changed at all. Every column is worth ten times the one to its right — and one tenth of the one to its left, which is the same fact read backwards and is the half children forget.
Group in threes
Do not read a long number left to right in one go. Group it in threes from the right.
2 480 619 becomes 2 | 480 | 619. Read each group and add its name: two million… four hundred and eighty thousand… six hundred and nineteen.
The spaces printed inside numbers on the paper are marking those groups for you. They are not decoration and they are not commas — use them.
The decimal trap
Multiplying and dividing by ten
Say the digits move, not the point.
Both descriptions give the right answer on easy examples, and only one survives. Move the point quietly becomes add a zero, which is fine for 47 × 10 and wrong for 4.7 × 10.
Every digit moving one column to the left is what is actually happening, and it costs nothing to say it correctly from the start.
Where do pupils lose marks?
Comparing decimals by length, which is the trap above.
Naming the wrong column in a long number, which grouping in threes prevents.
Losing the size of an answer — writing 46 when the answer was 46 000, usually after rounding.
Try it yourself
Group long numbers in threes from the right, and pad decimals so they have the same number of places.
- What is the 8 worth in 2 480 619?
- Write 306 042 in words.
- Put these in order, smallest first: 2.5, 2.05, 2.55
- Which is larger, 0.45 or 0.5?
- What is 4.7 multiplied by 10?
- 80 000. Group in threes from the right — 2 | 480 | 619 — and the 8 sits in the ten thousands column. Naming the column is the whole question.
- Three hundred and six thousand and forty-two. Group in threes: 306 | 042, then read each group and add its name.
- 2.05, 2.5, 2.55. Pad them to the same length first — 2.50, 2.05, 2.55 — and the order is obvious. Without padding, 2.05 looks longer than 2.5 and children put it last.
- 0.5. Pad it: 0.45 against 0.50. Four tenths is less than five tenths, and the 5 in the hundredths column cannot make up the difference. More digits does not mean bigger.
- 47. Every digit moves one column to the left. The point does not move — the digits do, which is worth insisting on because it is the version that keeps working with dividing.
How much practice does this type need at home?
Very little as a topic and a great deal as a habit, because place value turns up inside almost everything else.
The most useful drill takes ten seconds: say a long number and ask which column a particular digit is in. Then say two decimals and ask which is larger. Do the second one with awkward pairs — 0.4 and 0.35, 1.5 and 1.45 — because the easy pairs teach nothing.
Free: a Maths workbook
Questions across the Maths question types, with the method printed at the top and full answers at the back. One workbook for the whole strand, not a sheet per question type.
Frequently Asked Questions
Why does my child think 0.45 is bigger than 0.5?
Because 45 is bigger than 5, and for whole numbers more digits does mean bigger. Decimals break that rule, and nothing about how they look warns you. The fix is padding: write 0.45 and 0.50, so both have two decimal places, and compare column by column from the left. Four tenths against five tenths settles it before the second digit is even reached.
What is the point of grouping in threes?
It turns a long number into three short ones. Nobody reads 2480619 left to right in one go reliably. Group from the right — 2 | 480 | 619 — then read each group and add its name: two million, four hundred and eighty thousand, six hundred and nineteen. The spaces printed inside numbers on the paper are doing this for you already, and they are not decoration.
Should we say the digits move, or the point moves?
The digits move. Both descriptions get the right answer for multiplying by ten, but only one keeps working when the numbers get awkward, and 'move the point' quietly becomes 'add a zero', which fails on decimals. Every digit moving one column to the left is what is actually happening, and it is no harder to say.
How does this appear on the paper?
Rarely as a bare question. More often it is inside something else — ordering a set of measurements, deciding which of five amounts is closest to a value, or as the final step of a longer calculation where the answer has to be given to a stated accuracy. That is why we treat it as a foundation rather than a topic: it turns up wherever numbers do.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
We are not affiliated with, endorsed by or connected to GL Assessment or Buckinghamshire Council. Test arrangements change; always check the council's own pages for the current year's dates.
We Teach This Method Every Week in Winslow
Groups of no more than six pupils with two qualified teachers, in person or online. Come and see a session before you decide.