Numbers & Ordering — Grade 5 Mathematics
In Grade 5, we work with numbers up to one million, compare and order decimals with up to 3 places, identify prime and composite numbers, and use negative numbers in real-world contexts.
Place Value up to One Million
| Millions | H.Th | T.Th | Th | H | T | U | Tenths | Hundredths |
|---|---|---|---|---|---|---|---|---|
| 1 | 3 | 4 | 5 | 6 | 7 | 8 | ||
| 4 | 7 | . | 3 | 5 |
1 345 678 = one million, three hundred and forty-five thousand, six hundred and seventy-eight.
Ordering decimals: 4.73, 4.7, 4.07, 4.737
Compare digit by digit: units=4 (all equal) → tenths: 0.0, 0.7, 0.7, 0.7 → order: 4.07, 4.7, 4.73, 4.737
Ordering decimals: 4.73, 4.7, 4.07, 4.737
Compare digit by digit: units=4 (all equal) → tenths: 0.0, 0.7, 0.7, 0.7 → order: 4.07, 4.7, 4.73, 4.737
Prime and Composite Numbers
A prime number has exactly 2 factors: 1 and itself.
A composite number has more than 2 factors.
1 is neither prime nor composite.
A composite number has more than 2 factors.
1 is neither prime nor composite.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Orange = prime Grey = composite Dashed = neither
💡 Remember: 2 is the only even prime number.
Worked Examples
Example 1 — Read and Write in Words
Write 2 047 309 in words.
- 2 000 000 = two million
- 047 309 = forty-seven thousand, three hundred and nine
- Two million, forty-seven thousand, three hundred and nine
Example 2 — Order Decimals
Order from smallest to largest: 3.04, 3.4, 3.44, 3.404
- All have 3 units. Look at tenths: 0, 4, 4, 4
- 3.04 is smallest (tenths = 0)
- Others: hundredths 3.40, 3.44, 3.404 → 3.40 < 3.404 < 3.44
- 3.04, 3.4, 3.404, 3.44
Example 3 — Is 97 Prime? 🔍
Test whether 97 is prime.
- Test divisibility by primes up to √97 ≈ 9.8: try 2, 3, 5, 7.
- 97 is odd (not ÷2); 9+7=16, not ÷3; doesn't end in 0 or 5 (not ÷5); 97÷7≈13.9 (not exact)
- 97 is prime ✓
Practice Questions
1. What is the value of the digit 4 in 3 472 816?
✅ 4 is in the hundred-thousands position: value = 400 000
2. Order from largest to smallest: 5.6, 5.06, 5.605, 5.65.
✅ 5.65, 5.605, 5.6, 5.06
3. Write all prime numbers between 20 and 30.
✅ 23, 29
4. Is 51 prime? Explain.
✅ No. 51 = 3 × 17 — it has factors other than 1 and itself, so it is composite.
5. Write 3 056 204 in words.
✅ Three million, fifty-six thousand, two hundred and four
Key Points to Remember
- 1 million = 1 000 000 (seven digits, six zeros).
- When ordering decimals: compare digit by digit — left to right.
- A prime number has exactly 2 factors; a composite has more.
- 1 is neither prime nor composite; 2 is the only even prime.
- To test primality: try dividing by primes up to the square root of the number.