__CHAPTER 1__

__KNOWING OUR NUMBERS__

**COMPARING NUMBERS**

1. In a group of numbers, the one having the maximum number of digits is the greatest.

2. If two numbers have the same number of digits, say 5213 and 6421, we start comparing from thousands place. 6 is greater than 5. Therefore, 6421 is greater than 5213.

**ASCENDING ORDER**

When numbers are arranged from the smallest to the greatest, they are said to be in ascending order. E.g. 321, 426, 645, 1056

**DESCENDING ORDER**

When the numbers are arranged from the greatest to the smallest, they are said to be in descending order. E.g. 1056, 645, 426, 321

**INTRODUCING 10000**

The greatest 4 digit number is 9999. Adding 1 to it, we get 10000, a 5 digit number. We call it ten thousand.

Expansion of 5 digit numbers:

26212- Twenty six thousand two hundred twelve

**INTRODUCING 100000**

The greatest 5 digit number is 99999. Adding 1 to it, we get 100000, a 6 digit number called 1 lakh.

Expansion of 6 digit numbers:

452152- Four lakh fifty two thousand one hundred fifty two

**LARGER NUMBERS**

The largest 6 digit number is 999999. Adding 1 to it gives us 1000000 i.e. 10 lakh.

The largest 7 digit number is 9999999. Adding 1 to it gives us 10000000 i.e. 1 crore.

**INDIAN SYSTEM OF NUMERATION**

We use commas to mark thousands, lakhs and crores. The 1st comma is used to mark thousands and placed after 3 digits from the right. The 2nd comma is used to mark lakh and is placed after 5 digits from the right. The 3rd comma is used to mark crore and is placed after 7 digits from the right. E.g. 5,28,12,345

**INTERNATIONAL SYSTEM OF NUMERATION**

Commas are placed after every 3 digits from the right to mark thousands and millions.

**LARGE NUMBERS IN PRACTICE**

To measure length/distance, metre is used.

10 millimetres= 1 centimetres

100 centimetres= 1 metre

1 kilometre= 1000 metres

To measure weight, gram is used.

1000 milligram= 1 gram

1000 gram = 1 kilogram

To measure capacity, litre is used.

1000 millilitres= 1 litre

**APPROXIMATION**

Approximation is done when an accurate number cannot be obtained.

(i) Estimating to the nearest tens

Consider 18. Is it closer to 20 or to 10? 20, right? Therefore, 18 is rounded off to 20.

15, however, is equally close to 10 and 10. It is usually rounded off to 20.

(ii) Estimating to the nearest hundreds

Consider 620. Is it closer to 600 or to 700? It is closer to 600. Therefore, it is rounded off to 600.

(iii) Estimating to the nearest thousands

Consider 7215. It is closer to 7000 and is therefore, is rounded off to 7000.

**ROMAN NUMERALS**

Some major Roman numerals are:

1- I 100- C

5- V 500- D

10- X 1000- M

50- L

**The rules for this system are:**

- If a symbol is repeated, its value is added as many times it is repeated. E.g. III=3, XX=20
- A symbol is not repeated more than 3 times. The symbols V, L and D are, however, never repeated.
- If a symbol of a smaller value is written to the right of a greater value symbol, its value gets added to the greater value symbol. E.g. XIII= 10+3= 13
- If a symbol of smaller value is written to the left of a greater value symbol, its value gets subtracted from the greater value symbol. E.g. IX= 10-1= 9
- The symbols V, L and D are never written to the left of a symbol.
- The symbol I can be subtracted from V and X only.
- The symbol X can be subtracted from L, M and C only.

**Following these rules, let us see some basic Roman numerals:**

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

400= CD