Page 2 - LN-2

In this case, the decimal place is moved 6 places up until till it is placed after digit 7.
Therefore our standard form representation will be
−6
7×10
The exponents are also useful when converting the number from it’s standard form to
it’s natural form.

Comparison of Quantities Using Exponents

In-order to compare two large or small quantities, we convert them to their standard
exponential form and divide them.

For example : To compare the diameter of the earth and that of the sun.
6
Diameter of the Earth = 1.2756 × 10 m
9
Diameter of the Sun =1.4×10 m
9
Diameter of the Earth = 1.4×10 m
7
1.2756 × 10 m=109
So the diameter of the Sun is 109 times that of the Earth!

Note:While calculating the total or the difference between two quantities, we must first
ensure that the exponents of both the quantities are the same.

EXAMPLE - 1

Question 1.Write the following numbers in the expanded form:
(I)279404,

(II) 3006194,

Answer:
(i) 2,79,404 = 2,00,000 + 70,000 + 9,000 + 400 + 00 + 4

= 2 x 100000 + 7 x 10000 + 9 x 1000 + 4 x 100 + 0 x 10 + 4 x 1

5
3
4
2
1
0
= 2×10 + 7×10 + 9×10 + 4×10 + 0×10 + 4×10
(ii) 30,06,194 = 30,00,000 + 0 + 0 + 6,000 + 100 + 90 + 4
= 3 x 1000000 + 0 x 100000 + 0 x 10000 + 6 x 1000 + 1 x 100 + 9 x 10 +
4 x 1

2
1
0
3
4
6
5
= 3×10 + 0×10 + 0×10 + 6×10 + 1×10 + 9×10 + 4×10

EXAMPLE - 2