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Class 8 A Story of Numbers: cheat sheet
CBSE Mathematics. How people have written numbers: Roman numerals, Egyptian symbols, Mesopotamian base 60, Mayan base 20, and the Indian place value system with zero.
Key ideas
- Roman numerals add symbols, but a smaller symbol before a larger one is subtracted: IV = 4, XC = 90. There is no zero.
- Egyptian numbers repeat a symbol for each unit of each place: stroke 1, heel bone 10, coil of rope 100, lotus 1000, finger 10 000, tadpole 100 000.
- The Mesopotamians counted in base 60, which survives in 60 seconds and 60 minutes.
- The Maya counted in base 20 using a dot (1), a bar (5) and a shell for zero.
- The Indian system uses ten digits, place value and zero, so every number has a short, unique form.
- Zero as a number, with rules for adding and multiplying it, was set out by Brahmagupta.
Remember
| Roman symbols | I 1, V 5, X 10, L 50, C 100, D 500, M 1000 |
| Subtractive pairs | IV 4, IX 9, XL 40, XC 90, CD 400, CM 900 |
| Base 60 (two places) | value = first × 60 + second |
| Base 20 (two places) | value = first × 20 + second |
Watch out
- Writing IIII or VV instead of IV or X.
- Putting a smaller symbol before a much larger one: 99 is XCIX, not IC.
- Reading a base-60 or base-20 number as if it were base 10.
Worked example
Write 61434 with Egyptian symbols. How many symbols is that, compared with how many digits in our system?
Working: one symbol for each unit of each place; the digit sum counts them
Answer: 6 fingers, 1 lotus flower, 4 coils of rope, 3 heel bones and 4 strokes: 18 symbols vs 5 digits
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