# Decimal Representation Of Rational Numbers

## Decimal Representation Of Rational Numbers

Example 1:    Express (frac { 7 }{ 8 }) in the decimal form by long division method.

Solution:    We have,

∴ (frac { 7 }{ 8 }) = 0.875

Example 2:    Convert (frac { 35 }{ 16 }) into decimal form by long division  method.

Solution:    We have,

Example 3:    Express (frac { 2157 }{ 625 }) in the decimal form.

Solution:    We have,

Example 4:    Express (frac { -17 }{ 8 }) in decimal form by long division method.

Solution:    In order to convert (frac { -17 }{ 8 }) in the decimal form, we first express (frac { 17 }{ 8 }) in the decimal form and the decimal form of (frac { -17 }{ 8 }) will be negative of the decimal form of (frac { 17 }{ 8 })

we have,

Example 5:    Find the decimal representation of (frac { 8 }{ 3 }) .

Solution:    By long division, we have

Example 6:    Express (frac { 2 }{ 11 }) as a decimal fraction.

Solution:    By long division, we have

Example 7:    Find the decimal representation of (frac { -16 }{ 45 })

Solution:    By long division, we have

Example 8:    Find the decimal representation of (frac { 22 }{ 7 })

Solution:    By long division, we have

So division of rational number gives decimal expansion. This expansion represents two types

(A) Terminating (remainder = 0)

So these are terminating and non repeating (recurring)

(B) Non terminating recurring (repeating)

(remainder ≠ 0, but equal to devidend)

These expansion are not finished but digits are continusely repeated so we use a line on those digits, called bar ((bar{a})).

So we can say that rational numbers are of the form either terminating, non repeating or non terminating repeating (recurring).

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