MP Board Class 6 Mathematics

Chapter 1: Knowing Our Numbers (अपनी संख्याओं को जानना)

Quick Revision Notes & Formula Sheet

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1. Comparing Numbers (संख्याओं की तुलना)

• Rule 1: A number with more digits is always greater.
  • Example: 4532 > 897 (4 digits > 3 digits)
• Rule 2: If the number of digits is the same, compare the leftmost digits. If they are equal, compare the next digit to the right.
  • Example: 7854 > 7584 (Comparing hundred's place: 8 > 5)

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2. Ordering of Numbers (क्रम)

• Ascending Order (आरोही क्रम): Arrangement from the smallest to the greatest.
  • Example: 12, 45, 89, 102, 500
• Descending Order (अवरोही क्रम): Arrangement from the greatest to the smallest.
  • Example: 500, 102, 89, 45, 12

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3. Forming Numbers (संख्या बनाना)

• Greatest Number: Arrange the given digits in descending order.
• Smallest Number: Arrange the given digits in ascending order (Note: 0 cannot be placed at the extreme left).
  • Example with digits 4, 0, 7, 2:
    • Greatest Number = 7420
    • Smallest Number = 2047

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4. Number Systems & Place Value (संख्या पद्धति)

A. Indian Number System (भारतीय संख्या पद्धति)

• Periods: Ones, Thousands, Lakhs, Crores
• Comma Placement: First after 3 digits from the right, then after every 2 digits.
• Chart:

Ten Crore	Crore	Ten Lakh	Lakh	Ten Thousand	Thousand	Hundred	Ten	One
10,00,00,000	1,00,00,000	10,00,000	1,00,000	10,000	1,000	100	10	1

• Example: 5,43,21,098 (Five crore forty-three lakh twenty-one thousand ninety-eight)

B. International Number System (अंतर्राष्ट्रीय संख्या पद्धति)

• Periods: Ones, Thousands, Millions, Billions
• Comma Placement: After every 3 digits from the right.
• Chart:

Hundred Million	Ten Million	Million	Hundred Thousand	Ten Thousand	Thousand	Hundred	Ten	One
100,000,000	10,000,000	1,000,000	100,000	10,000	1,000	100	10	1

• Example: 54,321,098 (Fifty-four million three hundred twenty-one thousand ninety-eight)

C. Conversion Key:

• 1 Lakh = 100 Thousand
• 1 Million = 10 Lakhs
• 1 Crore = 10 Million
• 1 Billion = 1000 Million = 100 Crore

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5. Units of Measurement & Conversions (मापन की इकाइयां)

Length (लंबाई):

• 1 centimetre (cm) = 10 millimetres (mm)
• 1 metre (m) = 100 cm = 1,000 mm
• 1 kilometre (km) = 1,000 m = 1,00,000 cm = 10,00,000 mm

Mass/Weight (द्रव्यमान/भार):

• 1 gram (g) = 1,000 milligrams (mg)
• 1 kilogram (kg) = 1,000 g = 10,00,000 mg

Capacity/Volume (धारिता):

• 1 litre (L) = 1,000 millilitres (mL)
• 1 kilolitre (kL) = 1,000 L

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6. Estimation / Rounding Off (आकलन / सन्निकटन)

• Rounding off to Nearest 10:

  • Look at the ones digit.
  • If 0-4 $\rightarrow$ Round down (replace with 0).
  • If 5-9 $\rightarrow$ Round up (add 1 to tens place and replace ones digit with 0).
  • Example: 24 -> 20, 27 -> 30

• Rounding off to Nearest 100:

  • Look at the tens digit (or last two digits 00-49 vs 50-99).
  • Example: 841 -> 800, 286 -> 300

• Rounding off to Nearest 1000:

  • Look at the hundreds digit (or last three digits 000-499 vs 500-999).
  • Example: 7300 -> 7000, 7800 -> 8000

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7. Roman Numerals (रोमन संख्याएं)

Standard Symbols:

Symbol	I	V	X	L	C	D	M
Value	1	5	10	50	100	500	1000

Rules for Roman Numerals:

1. Repetition: If a symbol is repeated, its value is added. A symbol cannot be repeated more than 3 times.
   • III = 3, XXX = 30
2. Non-repeating symbols: V, L, and D are never repeated.
3. Addition: A smaller symbol written to the right of a larger symbol is added.
   • VI = 5 + 1 = 6, XII = 10 + 2 = 12, LXV = 50 + 10 + 5 = 65
4. Subtraction: A smaller symbol written to the left of a larger symbol is subtracted.
   • IV = 5 - 1 = 4, IX = 10 - 1 = 9, XL = 50 - 10 = 40, XC = 100 - 10 = 90
5. Subtraction Restrictions:
   • V, L, and D are never subtracted.
   • I can be subtracted from V and X only.
   • X can be subtracted from L, C, and M only.

Important Roman Numbers Quick Chart:

• 1 = I | 2 = II | 3 = III | 4 = IV | 5 = V
• 6 = VI | 7 = VII | 8 = VIII | 9 = IX | 10 = X
• 20 = XX | 30 = XXX | 40 = XL | 50 = L | 60 = LX
• 70 = LXX | 80 = LXXX | 90 = XC | 100 = C