CBSE Class 6 Maths — Knowing Our Numbers

Comparing Numbers

When comparing two numbers, we count the number of digits.

• The number with more digits is greater.
• If the number of digits is the same, compare the leftmost digits. The one with a larger leftmost digit is greater. If they match, move to the next digit on the right.

Number Systems

There are two major systems of reading and writing large numbers. Punctuation (commas) are used heavily to avoid confusion.

1. Indian System of Numeration

Commas are placed starting from the right. The first comma comes after hundreds place (3 digits). The next commas come after every two digits. Places: Ones, Thousands, Lakhs, Crores.

Example: 5,08,01,592 is read as Five crore eight lakh one thousand five hundred ninety-two.

2. International System of Numeration

Commas come after every three digits starting from the right. Places: Ones, Thousands, Millions, Billions. (1 Million = 10 Lakhs, 10 Million = 1 Crore).

Example: 50,801,592 is read as Fifty million eight hundred one thousand five hundred ninety-two.

Estimation (Rounding Off)

To make rapid calculations, we often round numbers out.

• Rounding to nearest 10: Look at unit digit. If < 5, replace by 0. If $\ge$ 5, increase ten’s digit by 1 and replace unit by 0. (e.g., 64 $\rightarrow$ 60, 67 $\rightarrow$ 70).
• Rounding to nearest 100: Look at ten’s digit. (e.g., 248 $\rightarrow$ 200, 269 $\rightarrow$ 300).
• Rounding to nearest 1000: Look at hundred’s digit. (e.g., 4256 $\rightarrow$ 4000, 4899 $\rightarrow$ 5000).

graph LR
    A[Number: 5,468] --> B{Rounding}
    B --> C[Nearest 10: 5,470]
    B --> D[Nearest 100: 5,500]
    B --> E[Nearest 1000: 5,000]

Roman Numerals

Before Hindu-Arabic numbers (0-9) existed, Romans used 7 basic letters to represent numbers.

Rules of Roman Numerals:

1. Only I, X, C, M can be repeated. They cannot be repeated more than 3 times (e.g., XXX = 30, but 40 is XL, not XXXX).
2. The symbols V, L, D are never repeated and never subtracted.
3. If a smaller symbol appears after a larger symbol, it is added (VI = 5 + 1 = 6).
4. If a smaller symbol appears before a larger symbol, it is subtracted (IX = 10 - 1 = 9).
5. Symbol I can be subtracted only from V and X. Symbol X can be subtracted only from L and C.