Number System & Simplification • Topic 1 of 6

Classification of Numbers

Numbers are organised into nested families: natural numbers (1, 2, 3, ...), whole numbers (0 included), integers (negatives too), rational numbers (any p/q with q not 0, including terminating and recurring decimals) and irrational numbers (non-terminating, non-repeating decimals such as root 2 or pi). A prime has exactly two factors; 1 is neither prime nor composite; 2 is the only even prime. Knowing where a number sits — and that there are 25 primes below 100 — answers many SSC one-liners instantly.

✅ Solved examples

1. How many prime numbers are there between 1 and 50?
They are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47 — count = 15.
2. Is 0.272727... rational or irrational?
A recurring decimal is rational. It equals 27/99 = 3/11, so it is rational.
3. Find the smallest prime number greater than 90.
91 = 7 x 13 (not prime), 92 to 96 composite, 97 is prime. Answer 97.
4. How many composite numbers lie between 10 and 20 (exclusive)?
Integers 11..19. Primes among them: 11,13,17,19 (4). Composite: 12,14,15,16,18 = 5.

✏️ Practice — try these, take hints as needed

1. How many primes lie between 50 and 70?
List odd candidates 53,59,61,67...
Check divisibility by 3 and 7.
Count them.
4 (53, 59, 61, 67)
2. Express 0.1666... as a fraction.
Recall 1/6 = 0.1666...
Or use the 10x trick.
Compare.
1/6
3. Which is irrational: 22/7, root 4, root 5, 0.25?
root 4 = 2.
root 5 is non-terminating non-repeating.
22/7 is a fraction.
root 5
4. The only even prime number is?
Every other even number is divisible by 2.
—
—
2
5. How many natural numbers from 1 to 30 are NOT prime?
Primes up to 30 = 10.
1 is not prime either.
30 - 10.
20

📝 Topic test — 8 questions

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