**Chapter Notes and Summary**

• **Notation : **Writing a number in figures is called notation.•

**Numeration :**Writing a number in words is called numeration.

**•**

**Digits or figures :**0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are called digits or figures.

**•**

**Numeral :**A group of digits, denoting a number, is called a numeral.

**•**

**Comparing numbers :**Two given numbers can be compared by counting their number of digits. number

**having more digits is greater than a number having less digits.**

**•**

**Ascending order :**In ascending order, numbers or quantities are arranged from lowest to largest.

**•**

**Descending order :**In descending order, numbers or quantities are arranged from highest to lowest.

**• In Hindu-Arabic place value system, we start from extreme right as; ones, tens, hundreds, thousands, ten**

**thousands, lakh, ten lakhs etc.**

**•**

**Periods :**Crore, lakh, thousand and hundred are known as periods.

**•**

**Separating periods in Hindu-Arabic system :**Crore, lakh thousands (hundreds + tens + ones).

**•**

**Face value of a digit :**face value of a digit remains as it is, whatever place it may be occupying in place

**value chart.**

**•**

**Place value of a digit :**place value of digit in a numeral depends upon place it occupies in place value

**chart.**

**•**

**International system of numerations :**

Periods Billions Millions Thousands OnesTen

Periods Billions Millions Thousands Ones

**billion**

**Billion Hundred**

**million**

**Ten**

**millions**

**Million Hundred**

**thousands**

**Ten**

**thousands**

**Thousands**

**Hundreds Tens Ones**

**T Ar Ar TCr Cr TL L T Th Th H T O**

**• 1 million = 10 lakh**

**• 10 million = 1 crore**

**• 1000 million = 100 crore or 1 arab**

**• number with less digits is less than number with more digits.**

**• units kilo is greatest and milli is smallest. Also, kilo shows 1000 times greater whereas milli shows 1000**

**times smaller and centi shows 100 times smaller.**

**• 1 kilometre = 1000 metre**

**• 1 kilogram = 1000 grams**

**• 1 metre = 10 decimetre = 100 centimetre = 1000 millimetre**

**• 1 gram = 10 decigram = 100 centigram = 1000 milligram.**

**• 1 litre = 10 decilitre = 100 centilitre = 1000 millilitre.**

**• In above figure, each unit has difference of 10.**

**i.e., 1 kilometre = 10 hectometre**

**and 1 kilometre = 10 × 10 decametre**

**• Estimation means approximating a quantity to an accuracy required.**

**•**

**Roman numbers :**

Roman NumeralI V X L C D M

Roman Numeral

**Hindu-Arabic Numeral**1 5 10 50 100 500 1000

**• If a bar is places over a numeral, it is multiplied by 1000. Thus V = 5000, X = 10000 etc.**

**• Repetition of a Roman numeral means addition.**

**(i) Only I, X, C, M can be repeated**

Note :

Note :

**(ii) V, L and D are never repeated.**

**(iii) No symbol (Roman numeral) can be repeated more than 3 times.**

**• A smaller numeral written to right of larger numeral is always added to larger numeral.**

**• A smaller numeral written to left of a larger numeral is always subtracted from larger numeral.**

**(i) V, L and D are never subtracted.**

Note :

Note :

**(ii) I can be subtracted from V and X only.**

**(iii) X can be subtracted from L and C only.**

**(iv) C can be subtracted from D and M only.**

**• When a smaller numeral is placed between two larger numerals, it is always subtracted from larger numeral**

**immediately.**