Posted on : 19-11-2017 Posted by : Admin

When two numbers are given,

- The number with more digits is greatest.
- If number of digits is same, then the number with greater leftmost digit is greatest
- If number of digits is also same, then examine the next digit from left and so on.

- To form different numbers from given digits,
- No digit must be repeated
- All the given digits must be used
- For example, take four digits 7, 8, 3, 5
- The greatest number we get is 8753
- The smallest number we can get is 3578
- To make greatest number, arrange digits in descending order.
- To make smallest number, arrange digits in ascending order except zero. Zero can occupy any place except leftmost place.
- When we shift the digits from one place to other, the number can become large or sometimes even small.

**Ascending order –** The arrangement from the smallest to the greatest

**Descending order –** The arrangement from the greatest to the smallest

- The smallest two-digit number is 10 (ten) and it follows the largest one digit number 9
- The smallest three-digit number is 100 (one hundred) and it follows the largest two digit number 99
- The smallest four-digit number is 1,000 (one thousand) and it follows the largest three digit number 999
- The smallest five digit number is 10,000 (ten thousand) and it follows the largest four digit number 9,999
- The smallest six digit number is 100,000 (one lakh) and it follows the largest five-digit number 99,999 and so on.

Look at the pattern: 9 + 1 = 10 = 10 × 1

99 + 1 = 100 = 10 × 10

999 + 1 = 1000 = 10 × 100

9999 + 1 = 10000 = 10 x 1000

We observe that,

Greatest single digit number + 1 = smallest 2-digit number

Greatest 2-digit number + 1 = smallest 3-digit number

Greatest 3-digit number + 1 = smallest 4-digit number and so on.

Use of commas helps in reading and writing large numbers. In India, Hindu-Arabic numeral system and also Roman numeral system are used.

In the Indian system of numbers,

- We use ones, tens, hundreds, thousands, lakhs and crores
- Commas are placed after 3 digits starting from the right and then every 2 digits thereafter. Commas are used to mark hundreds, thousands, lakhs and crores. For example: 12, 34, 56, 789
- The commas after 3, 5 and 7 digits separate thousand, lakh and crores respectively

In the International system of numbers,

- We use ones, tens, hundreds, thousands and millions
- Commas are placed after every 3 digits starting from the right to mark hundreds, thousands and millions, billions. For example: 123, 456, 789
- The commas after 3 and 6 digits separate thousand and million respectively.

**Click for more info on Number systems**

- The estimation refers to the approximation. The estimate gives rough idea before the exact value.
- In a number of situations we do not need the exact quantity but only a reasonable guess or an estimate would be enough.
- For example, while stating how many kilometers is the school from the house, we state the approximate number; may be 3 or 5 km we do not need to state the exact number.
- Estimation is useful in a number of situations, when we need a quick and rough answer. It is useful in checking answers.
- In estimating the products, it is a general rule to, Round off each factor to its greatest place, then multiply the rounded off factors.

- Estimating to the nearest tens by rounding off

Numbers 1 to 4 are rounded off to 0 and numbers 5 to 9 are rounded off to 10.

- Estimating to the nearest hundreds by rounding off

Numbers 1 to 49 are rounded off to 0 and numbers 50 to 99 are rounded off to 100.

- Estimating to the nearest thousands by rounding off

Numbers 1 to 499 are rounded off to 0 and numbers 500 to 999 are rounded off to 1000.

- We perform various functions on the numbers like addition, subtraction, multiplication, division etc.
- Sometimes we may have to execute many functions together. To avoid confusion while doing so, brackets are used.
- The numbers on which we perform the same function are packed into a bracket and are treated as a single number.
- While solving the problems with brackets, first turn everything inside the brackets into a single number and then do the operations outside the brackets

- In India we use Hindu-Arabic numeral system. Other than this, there are many other numeral systems
- Roman numeral system is one of the oldest systems of writing numerals.
- This system uses the following special symbols to represent numbers.
- Other roman numerals are formed by the combination of these special symbols
- The rules for the system are:

- If a symbol is repeated, its value is added as many times as it occurs:

**Ex:** II is equal 2, XX is 20 and XXX is 30.

- A symbol is not repeated more than three times. And the symbols V, L and D are never repeated.

**Ex:** We do not write VV to resemble 10, Instead we have a symbol for 10 that is X; Similarly we do not write LL to resemble 100, instead we have a symbol for 100 that is C and so on

- If a symbol of smaller value is written to the right of a symbol of greater value, its value gets added to the value of greater symbol.

**Ex:** VI = 5 + 1 = 6, XII = 10 + 2 = 12 and LXV = 50 + 10 + 5 = 65

- If a symbol of smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of the greater symbol.

**Ex:** IV = 5 – 1 = 4, IX = 10 – 1 = 9

XL= 50 – 10 = 40, XC = 100 – 10 = 90

- The symbols V, L and D are never written to the left of a symbol of greater value, i.e. V, L and D are never subtracted.

**Ex:** The symbol I can be subtracted from V and X only.

The symbol X can be subtracted from L, M and C only.

Other roman numerals are formed by the combination of these special symbols,

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**Click for more info on Romal numbers**

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