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Place value is the foundation of all number work. In the SET 11+ exam, both Stage 1 (multiple-choice) and Stage 2 (written paper) test your ability to read, write, compare, and order numbers with confidence. Getting place value right means fewer mistakes and faster working throughout the rest of the paper.
Every digit in a number has a value that depends on its position (or place). The further left a digit sits, the greater its value.
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|---|---|---|---|
| 1,000,000 | 100,000 | 10,000 | 1,000 | 100 | 10 | 1 | . | 0.1 | 0.01 | 0.001 |
For example, in the number 3,472,609:
| Digit | Place | Value |
|---|---|---|
| 3 | Millions | 3,000,000 |
| 4 | Hundred Thousands | 400,000 |
| 7 | Ten Thousands | 70,000 |
| 2 | Thousands | 2,000 |
| 6 | Hundreds | 600 |
| 0 | Tens | 0 |
| 9 | Ones | 9 |
Key Point: When a question asks "What is the value of the digit 7 in 3,472,609?", the answer is 70,000 — not just 7. Always give the full place value.
Read large numbers by splitting them into groups of three digits from the right. Each group has a label: ones, thousands, millions.
You need to go both ways confidently:
Watch out: Zeros are place-holders. In 2,060,300 there are zeros in the hundred-thousands, thousands, tens, and ones places. Every zero matters!
| Symbol | Meaning | Example |
|---|---|---|
| > | Greater than | 8,743 > 7,899 |
| < | Less than | 3,200 < 3,210 |
| = | Equal to | 450 = 450 |
Put these numbers in order from smallest to largest: 56,482 — 56,248 — 56,842 — 56,428
Step 1: All four numbers start with 56, so compare the hundreds digit.
Step 2: The hundreds digits are 4, 2, 8, and 4. The number with 8 in the hundreds (56,842) is the largest, and the number with 2 in the hundreds (56,248) is the smallest.
Step 3: Two numbers have 4 in the hundreds: 56,482 and 56,428. Compare the tens digit: 8 > 2, so 56,482 > 56,428.
Answer: 56,248, 56,428, 56,482, 56,842
Decimal numbers follow the same rules, but take extra care with the number of decimal places.
Put in order from smallest to largest: 0.62, 0.602, 0.7, 0.062
Step 1: Write all numbers with the same number of decimal places: 0.620, 0.602, 0.700, 0.062.
Step 2: Now compare as whole numbers: 620, 602, 700, 062.
Answer: 0.062, 0.602, 0.62, 0.7
SET Tip: On Stage 1, you only need to identify the correct answer from four options, so quickly ruling out obviously wrong orderings will save time.
Partitioning means breaking a number into parts based on place value.
Partitioning is a powerful tool for mental calculations — a skill tested throughout the SET.
Use partitioning to calculate 4,538 + 2,347.
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 4,000 + 2,000 = 6,000 | 500 + 300 = 800 | 30 + 40 = 70 | 8 + 7 = 15 |
Combine: 6,000 + 800 + 70 + 15 = 6,885
You may be asked to read values from a number line or a measuring scale. The key skill is working out what each interval represents.
A number line goes from 0 to 200. It is divided into 10 equal parts. An arrow points to the third mark. What number is the arrow pointing to?
Each part = 200 ÷ 10 = 20. The third mark = 3 × 20 = 60.
Place value and ordering underpin everything in arithmetic. Make sure you can: identify the value of any digit in a number, read and write numbers in words and figures, compare and order whole numbers and decimals, partition numbers for mental calculations, and read scales and number lines. Mastering these skills will help you answer quickly and accurately on both stages of the SET, where every mark counts.