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Place Value and Ordering
Place Value and Ordering
Place value is the very foundation of arithmetic. If you can read, write, and compare numbers confidently, you will save precious time on the CSSE maths paper. The CSSE exam includes one maths paper that covers both arithmetic and problem-solving, so being fast and accurate with place value is essential.
What Is Place Value?
Every digit in a number has a value determined by its position. 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 2,685,413:
| Digit | Place | Value |
|---|---|---|
| 2 | Millions | 2,000,000 |
| 6 | Hundred Thousands | 600,000 |
| 8 | Ten Thousands | 80,000 |
| 5 | Thousands | 5,000 |
| 4 | Hundreds | 400 |
| 1 | Tens | 10 |
| 3 | Ones | 3 |
Key Point: When a CSSE question asks "What is the value of the digit 8 in 2,685,413?", the answer is 80,000 — not just 8. Always give the full place value.
Reading and Writing Large Numbers
Splitting numbers into groups
Read numbers by splitting them into groups of three digits from the right. Each group gets a label: ones, thousands, millions.
- 3,207,540 is read as "three million, two hundred and seven thousand, five hundred and forty."
Converting between words and figures
You need to be comfortable going both ways:
- Words to figures: "Four hundred and twelve thousand, nine hundred and six" = 412,906
- Figures to words: 5,030,800 = "Five million, thirty thousand, eight hundred"
Watch out: Zeros are place-holders. In 5,030,800 there are zeros in the hundred-thousands, thousands, tens, and ones places. Every zero matters!
Ordering and Comparing Numbers
Inequality symbols
| Symbol | Meaning | Example |
|---|---|---|
| > | Greater than | 7,432 > 6,987 |
| < | Less than | 2,100 < 2,110 |
| = | Equal to | 500 = 500 |
Worked Example
Put these numbers in order from smallest to largest: 47,382 — 47,238 — 47,832 — 47,328
Step 1: All four numbers start with 47, so compare the hundreds digit.
Step 2: The hundreds digits are 3, 2, 8, and 3. The number with 8 in the hundreds place (47,832) is the largest.
Step 3: Two numbers have 3 in the hundreds place: 47,382 and 47,328. Compare the tens digit: 8 > 2, so 47,382 > 47,328.
Step 4: 47,238 has the smallest hundreds digit (2), so it is the smallest overall.
Answer: 47,238, 47,328, 47,382, 47,832
Ordering Decimals
Decimal numbers follow the same rules, but take extra care with the number of decimal places.
Worked Example
Put in order from smallest to largest: 0.45, 0.405, 0.5, 0.045
Step 1: Write all numbers with the same number of decimal places: 0.450, 0.405, 0.500, 0.045.
Step 2: Now compare as if they were whole numbers: 45, 405, 500, 450.
Wait — let us be more careful. With three decimal places they become: 450, 405, 500, 045.
Answer: 0.045, 0.405, 0.45, 0.5
CSSE Tip: Multi-step word problems on the CSSE paper often require you to compare values before doing further calculations. Getting the ordering right first will save you from careless errors.
Partitioning Numbers
Partitioning means breaking a number into parts based on place value.
- 6,453 = 6,000 + 400 + 50 + 3
- 2.75 = 2 + 0.7 + 0.05
Partitioning is especially helpful for mental addition and subtraction — skills that are tested heavily on the CSSE paper.
Worked Example
Use partitioning to calculate 3,247 + 1,538.
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 3,000 + 1,000 = 4,000 | 200 + 500 = 700 | 40 + 30 = 70 | 7 + 8 = 15 |
Combine: 4,000 + 700 + 70 + 15 = 4,785
Number Lines and Scales
You may be asked to read values from a number line or scale. The key skill is working out what each interval represents.
Worked Example
A number line goes from 0 to 100. It is divided into 5 equal parts. An arrow points to the second mark. What number is the arrow pointing to?
Each part = 100 ÷ 5 = 20. The second mark = 2 × 20 = 40.
Summary
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 work quickly and accurately on the CSSE maths paper, where every second counts.