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Exponents and Powers

    Decimal Number System

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7th class > Exponents and Powers > Decimal Number System

Decimal Number System

T Th
Th
H
T
O
4
7
5
6
1
1
×
1
=
1
6
×
10
=
60
5
×
100
=
500
7
×
1000
=
7000
4
×
10000
=
40000

Let us look at the expansion of 47561, which we already know:

47561 = 4 × + 7 × + 5 × + 6 × + 1

We can express it using powers of 10 in the exponent form:

Therefore, 47561=4× 10 +7× 10 +5× 10 +6× 10 +1× 10

Note: 10,000 = 104, 1000 = 103, 100 = 102, 10 = 101 and 1 = 100

Let us expand another number:

L
TTh
Th
H
T
O
1
0
4
2
7
8
8
×
1
=
8
7
×
10
=
70
2
×
100
=
200
4
×
1000
=
4000
0
×
10000
=
0
1
×
100000
=
100000

undefined

104278 = 1 × 100,000 + 0 × 10,000 + 4 × 1000 + 2 × 100 + 7 × 10 + 8 × 1

= 1 × 105 + 0 × 104 + 4 × 103 + 2 × 102 + 7 × 101+ 8 × 100

= 1 × 10 + 4 × 10 + 2 × 10 + 7 × 10 + 8 × 10

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.