NCERT Class 7 Mathematics

EXPONENTS AND POWERS 261

4. Express each of the following as a product of prime factors only in exponential form:
   (i) 108 × 192 (ii) 2 7 0 (iii) 729 × 64
   (iv) 768


5. Simplify:

(i)  

532

3

27

87





(ii)

25 5

10

28

34

××

×

t

t

(iii)

55

75

310 25

56

13.5 DECIMAL NUMBER SYSTEM

Let us look at the expansion of 47561, which we already know:
47561 = 4 × 10000 + 7 × 1000 + 5 × 100 + 6 × 10 + 1
We can express it using powers of 10 in the exponent form:

Therefore, 47561 = 4 × 10^4 + 7 × 10^3 + 5 × 10^2 + 6 × 10^1 + 1 × 10^0
(Note 10,000 = 10^4 , 1000 = 10^3 , 100 = 10^2 , 10 = 10^1 and 1 = 10^0 )
Let us expand another number:
104278 = 1 × 100,000 + 0 × 10,000 + 4 × 1000 + 2 × 100 + 7 × 10 + 8 × 1
= 1 × 10^5 + 0 × 10^4 + 4 × 10^3 + 2 × 10^2 + 7 × 10^1 + 8 × 10^0
= 1 × 10^5 + 4 × 10^3 + 2 × 10^2 + 7 × 10^1 + 8 × 10^0
Notice how the exponents of 10 start from a maximum value of 5 and go on decreasing
by 1 at a step from the left to the right upto 0.

13.6 EXPRESSING LARGE NUMBERS IN THE STANDARD FORM
Let us now go back to the beginning of the chapter. We said that large numbers can be
conveniently expressed using exponents. We have not as yet shown this. We shall do so now.

1. Sun is located 300,000,000,000,000,000,000 m from the centre of our Milky Way
   Galaxy.


2. Number of stars in our Galaxy is 100,000,000,000.


3. Mass of the Earth is 5,976,000,000,000,000,000,000,000 kg.
   These numbers are not convenient to write and read. To make it convenient
   we use powers.
   Observe the following:
   59 = 5.9 × 10 = 5.9 × 10^1
   590 = 5.9 × 100 = 5.9 × 10^2
   5900 = 5.9 × 1000 = 5.9 × 10^3
   5900 = 5.9 × 10000 = 5.9 × 10^4 and so on.

TRY THESE

Expand by expressing

powers of 10 in the

exponential form:

(i) 172

(ii) 5,643

(iii) 56,439

(iv) 1,76,428