Page 106 - Maths Skills - 7

104 Maths

INTRODUCTION
Observe the following mathematical expressions:
● The weight of the planet earth is 5.972 × 10 kg.
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● The distance of the earth from the sun is 150,000,000 km.
● Light travels at a speed of 3 × 10 m/s.
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● The memory of the hard disc in my computer is 2 GB.
These very large numbers also shows the easier way of representing them.
Thus, exponential notation or power notation is a scientific way of writing large numbers as well as extremely
small numbers.

EXPONENTS

Exponents help in writing the large numbers in a shorter form which we can read, understand and compare easily.
Let’s see few examples:
(i) 2 × 2 × 2 × 2 × 2 × 2 can be written as 2 . (ii) 3 × 3 × 3 × 3 can be written as 3 .
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(iii) 5 × 5 can be written as 5 .
2
5 → exponent

Base
Here, 10 →
Power
Power consists of two parts, i.e. a base number and the exponent.
Thus, 10 is the exponential form of 100000.
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We can write 1024 in exponential form as 1024 = 2 ×2 ×2 ×2 ×2 ×2 ×2 ×2 ×2 ×2 = 2 10

In this case, 2 is the base and 10 is exponent (or index). Exponents can be used in writing expanded form of large
numbers. For example, 2456728390 is written as:
2 × 1,000,000,000 + 4 × 100,000,00 + 5 × 10,000,000 + 6 × 1,000,000 + 7 × 100,000 + 2 × 10000
+ 8 × 1000 + 3 × 100 + 9 × 10

= 2 × 10 + 4 × 10 + 5 × 10 + 6 × 10 + 7 × 10 + 2 × 10 + 8 × 10 + 3 × 10 + 9 × 10 1
7
8
9
6
3
2
5
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Remember that a base can be any sort of number, i.e., a whole number, a decimal number or a rational number,
for example;
(i) 7 × 7 × 7 = 7 and is read as ‘seven cubed’.
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(ii) (–1) × (–1) × (–1) × (–1) = (–1) and is read as (–1) raised to the power 4.
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1 1 1 1 1  1  5 1
(iii) × × × × =   and is read as raised to the power 5.
5 5 5 5 5  5  5
POWERS OF NEGATIVE INTEGERS
Study the following examples. Fact-o-meter

(i) (–1) = – 1 � Any number to the power one
1
is the number itself. i.e. x = x
1
(ii) (–1) = (–1) × (–1) = 1 � Any number to the power zero
2
0
(iii) (–1) = (–1) × (–1) × (–1) = – 1 is 1. i.e. x = 1
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