Numbers & the Number System • Topic 9 of 9

Roman Numerals (Basic)

Roman numerals are the symbol system of ancient Rome, still seen on clocks, chapter headings and monuments. At the primary level five symbols matter: I = 1, V = 5, X = 10, L = 50, C = 100. Numbers are built by three rules. The addition rule: a smaller symbol written after (to the right of) a larger one is added, so VI = 5 + 1 = 6 and LXV = 50 + 10 + 5 = 65. The subtraction rule: a smaller symbol written before (to the left of) a larger one is subtracted, so IV = 5 - 1 = 4, IX = 9, XL = 40 and XC = 90 - but only I, X and C are ever subtracted (I from V and X; X from L and C), and V and L are never subtracted. The repetition rule: I, X and C may repeat up to three times to add up (III = 3, XXX = 30), while V and L are never repeated; this is why 4 is IV and never IIII. Symbols normally run largest to smallest, left to right. So XIV reads as X (10) + IV (4) = 14, and XCIX reads as XC (90) + IX (9) = 99.

✅ Solved examples

1. Convert XIV to a Hindu-Arabic number.

XIV = X + IV = 10 + 4 = 14. The IV uses the subtraction rule (1 before 5 = 4).

2. Why is 4 written as IV and not IIII?

A symbol may repeat at most three times, so IIII is invalid. The subtraction rule gives IV = 5 - 1 = 4 instead.

3. Convert XCIX to a number.

XCIX = XC + IX = 90 + 9 = 99. XC is 100 - 10 = 90 and IX is 10 - 1 = 9.

4. Write 65 in Roman numerals.

LXV = 50 + 10 + 5 = 65, using the addition rule with symbols in largest-to-smallest order.

✏️ Practice — try these, take hints as needed

1. Convert XL to a number.

X before L subtracts.

50 - 10.

2. Convert LXXVIII to a number.

L is 50, XX is 20, V is 5, III is 3.

Add them in order.

3. Write 9 in Roman numerals.

Use the subtraction rule.

1 before 10.

4. Convert XXV to a number.

Two tens then a five.

10 + 10 + 5.

📝 Topic test — 8 questions

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Key Concepts — Quick Reference

This chapter

Place value (base-10 columns and the two values of a digit)

Ones	1st place from right = 10^0 = 1
Tens	2nd place from right = 10^1 = 10
Hundreds	3rd place from right = 10^2 = 100
Thousands	4th place from right = 10^3 = 1000
Face value	The digit itself, ignoring position. In 3582 the face value of 8 is 8.
Place value	Face value x value of its place. In 3582 the place value of 8 is 8 x 10 = 80.

Roman numerals and parity rules

Roman symbols	I = 1, V = 5, X = 10, L = 50, C = 100
Add / subtract rule	Smaller after larger adds (VI = 6); smaller before larger subtracts (IV = 4, IX = 9, XL = 40, XC = 90)
Repetition rule	I, X, C repeat up to three times; V and L are never repeated and never subtracted
Even number	Ends in 0, 2, 4, 6 or 8; can be written as 2n
Odd number	Ends in 1, 3, 5, 7 or 9; can be written as 2n + 1