**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).