3. Estimation of Numbers

USING BRACKETS
Meera bought 6 notebooks from the market and the cost was Rs 10 per notebook. Her sister Seema also bought 7 notebooks of the same type. Find the total money they paid.
Seema calculated the 
6 × 10 + 7 × 10 = 60 + 70 = 130 
Meera calculated the amount like this amount like this
6 + 7 =13  and 13 × 10 = 130
 Ans. Rs 130.

We can see that Seema’s and Meera’s ways to get the answer are a bit different. 
To avoid confusion in such cases we may use brackets. We can pack the numbers 6 and 7 together using a bracket, indicating that the pack is to be treated as a single number. 
Thus, the answer is found by (6 + 7) × 10 = 13 × 10.
First, turn everything inside the brackets ( ) into a single number and then do the operation outside which in this case is to multiply by 10.

FACE VALUE
Face value of a digit in a numeral is the value of the digit itself at whatever place it may be. 

PLACE VALUE
Place value of a digit in a given number is the value of the digit because of the place or the position of the digit in the number.
Place value of a digit = Face value of the digit  × value of the place  

Place value and Face value :
Every digit has two values – the place value and the face value. The face value of a digit does not change while its place value changes according to its position and number. 

Expanded form of a Number :
If we express a given number as the sum of its place value, it is called its expanded form. 

Ex:    Express 
        (i) 3,64,029    (ii) 2,75,00,386 in expanded form. 
Sol.  Place value of 3 = 3 x 100000 
        Place value of 6 = 6 x 10000
        Place value of 4 = 4 x 1000
        Place value of 0 = 0 x 100
        Place value of 2 = 2 x 10 
        Place value of 9 = 9 x 1
 ∴    The expanded form of 3,64,029 is  
        3 x 100000 + 6 x 10000 + 4 x 1000 + 0 x 100 + 2 x 10 + 9 x 1.