# Decimal Number System Using Exponents and Powers:

Decimal numbers can be expanded using exponents and powers.

Example 1,

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 × 105 + 4 × 103 + 2 × 102 + 7 × 101 + 8 × 100.

(Note 100,000 = 105, 10,000 = 104, 1000 = 103, 100 = 102, 10 = 101 and 1 = 100)

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 up to 0.

Example 2,

1425.36 = 1 × 1000 + 4 × 100 + 2 × 10 + 5 × 1 + 3/10 + 6/100

= 1 × 10 3 + 4 × 10 2 + 2 × 10 + 5 × 1 + 3 × 10 – 1 + 6 × 10– 2.

#### Example

Expand the following numbers using exponents.

1025.63

1025.63 = 1 × 1000 + 0 × 100 + 2 × 10 + 5 × 1 + 6/10 + 3/100.

= 1 × 103 + 0 × 102 + 2 × 101 + 5 × 10° + 6 × 10-1 + 3 × 10-2.

#### Example

Expand the following numbers using exponents.

1256.249

1256.249 = 1 × 1000 + 2 × 100 + 5 × 10 + 6 × 1 + 2/10 + 4/100 + 9/1000

= 1 × 103 + 2 × 102 + 5 × 101 + 6 × 10° + 2 × 10-1 + 4 × 10-2 + 9 × 10-3.

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