- The
**place value**of a digit in a number is the value it holds at the place in the number. If 2 is at hundred-place in a number, its place value will be 200, if 5 is at thousand-place, its value will be 5000 etc. - The
**face value**of a digit is the digit itself, at whatever place it may be. It is unchangeable and definite. - Place value changes according to the digit’s place but face value does not.
- The place value of the digit decreases by tens as it moves from left to right. For instance the place value of the digit 4 in the number 14,560 is 4,000. When it is shifted to 15,460 the place of the digit 4 is now 400.

- In
**Indian Number System**, we use different periods like**ones**,**thousands**,**lakhs**,**crores**, etc.

- 1 = One
- 10 = Ten
- 100 = Hundred
- 1,000 = One thousand
- 10,000 = Ten Thousand
- 1,00,000 = One lakh
- 10,00,000 = Ten lakh
- 1,00,00,000 = One crore

- The Indian numbering system uses seperators differently from the international norm; a comma divides every two rather than every three digits to the left of the last three, that is after hundreds.
- For Example 5,00,000, 12,12,12,123

**International system**is followed by most of the countries of the world. In this system, a number is split up into groups or periods.In the Inter-national System of Numeration, we use**ones**,**tens**,**hundreds**,**thousands**,**millions**and**billions**.- 1 = One
- 10 = Ten
- 100 = Hundred
- 1,000 = One thousand
- 10,000 = Ten Thousand
- 1,00,000 = Hundred Thousand
- 10,00,000 = One Million
- 1,00,00,000 = Ten Million
**The 1st period consists of ---> ones, tens and hundred.**

The 2nd period consists of ---> thousand, 10 thousand and 100 thousands.

The 3rd period consists of ---> million, 10 million and 100 million.

The 4th period consists of ---> billion, 10 billion and 100 billion.

- The
**Roman numerals**are as follows –

I | V | X | L | C | D | M |

1 | 5 | 10 | 50 | 100 | 500 | 1000 |

- The Roman numbers follow certain rules, which helps determine how the number is written.
- When a symbol is repeated, its value is added as many times as it occurs. For example, III=3, XX=20 etc.
- Symbols cannot be repeated more than three times e.g. the Roman numeral for 395 is CCCXCV.
- The symbols V, L and D are never repeated.
- If a smaller symbol is written to the right of a symbol with greater value, then its value gets added to the value of the greater symbol. For example, VI=5+1=6, XI=11 and so on.
- If a smaller symbol is written on the left of a symbol with greater value, then its value is subtracted from the value of the greater symbol. IV= 5-1=4, IX=9 etc.
- The symbols V, L and D are never written to the left of a symbol of greater value. It means V, L and D are never subtracted.
- The symbol I can be subtracted from V and X only.
- The symbol X can be subtracted from L, M, and C only.
- We cannot repeat a symbol on the left side of a symbol to subtract, more than once eg. 98 is written as XCVIII and not as IIC.

**Large numbers**are needed in many fields. It may be calculation of number of students in a school, population census of a city, ascertainment of profits of big corporate houses etc.**Estimation**: At many a times we do not need the exact quantity or numbers, but only an estimate. For instance it could be the number of spectators watching cricket match, an estimate of the number of hair on the head etc.