Numbers Ordering — Grade 4 Mathematics
In Grade 4, we work with numbers up to 100 000 and introduce negative numbers. We read and write Roman numerals, understand the value of digits in 5-digit numbers, and place any integer on a number line.
5-Digit Numbers — Place Value
A 5-digit number uses: Ten-Thousands (TTh), Thousands (Th), Hundreds (H), Tens (T), Ones (O).
Example: 64 329 = 60 000 + 4 000 + 300 + 20 + 9
The number is read: "sixty-four thousand, three hundred and twenty-nine"
Example: 64 329 = 60 000 + 4 000 + 300 + 20 + 9
The number is read: "sixty-four thousand, three hundred and twenty-nine"
Negative Numbers
Numbers below zero are negative — written with a minus sign: −5, −12, −100.
On a number line, negative numbers sit to the left of zero.
Ordering rule: −10 < −3 < 0 < 5 < 12 (further left = smaller)
On a number line, negative numbers sit to the left of zero.
Ordering rule: −10 < −3 < 0 < 5 < 12 (further left = smaller)
−10
−5
0
5
10
💡 Temperature: A common real-world context — −5°C is colder than 3°C. The difference is 3 − (−5) = 8 degrees.
Worked Examples
Example 1 — Ordering 5-Digit Numbers
Order from smallest to largest: 54 209, 54 029, 54 920, 54 290
- All start with 54 (TTh, Th same). Look at H: 2, 0, 9, 2
- H=0: 54 029 (smallest)
- H=2: 54 209 and 54 290 — compare T: 0 < 9
- H=9: 54 920 (largest)
- Order: 54 029, 54 209, 54 290, 54 920
Example 2 — Ordering Negative Numbers
Order from smallest to largest: 3, −7, 0, −2, 8, −15
- Place on number line: −15, −7, −2, 0, 3, 8
- Order: −15, −7, −2, 0, 3, 8
Example 3 — Real World: Temperature Changes 🌡️
At midnight it was −8°C. By noon it had risen 15°C. What was the noon temperature?
- −8 + 15 = 7°C
- The temperature went from below zero to above zero.
Practice Questions
1. Write 83 047 in expanded form.
✅ 80 000 + 3 000 + 0 + 40 + 7 = 83 047
2. Which is colder: −3°C or −9°C?
✅ −9°C is colder (further left on the number line)
3. Order smallest to largest: 72 450, 27 540, 72 045, 27 054
✅ 27 054, 27 540, 72 045, 72 450
4. The temperature is −6°C. It drops another 4°C. What is the new temperature?
✅ −6 − 4 = −10°C
5. What is the largest 5-digit even number using digits 1, 3, 5, 7, 8?
✅ Last digit must be even (8): arrange remaining digits 7, 5, 3, 1 in descending order → 75 318
Key Points to Remember
- 5-digit numbers go up to 99 999; the next is 100 000 (six digits).
- Negative numbers are less than zero; they increase in size moving left on the number line.
- −8 < −3 because −8 is further left (colder, deeper in debt, etc.).
- To find the difference between a positive and negative temperature: add the absolute values.
- Always compare from the highest place value first when ordering.