There are two types of rational no.

1) finite or terminating decimal 2) Non terminating decimals.

Conversion of rational no. to decimals

1)

Express 7 / 8 rational numbers to decimals form by long division method.

7 / 8 = 0.875

Express - 17 / 8 in the decimal form by long division method.

- 17 / 8 = - 2.125

Express 8 / 3 in the decimal form by long division method.

8 / 3 = 2.6666

_⇒ 2.6 |

Such a decimal numbers are known as non-terminating decimals.

2)

a) A decimal in which all the digits after the decimal point are repeated. These type of decimals are known as pure recurring decimals.

Example :

_ __o.6, 0.16 |

1) Obtain the repeating decimal and put it equal to x.(say)

2) Write the number without using bar and equal to x.

3) Determine the number of digits having bar on their heads or number of digits before the bar for mixed recurring decimal.

4) If the repeating number is 1 then multiply by 10; if repeating number is 10 then multiply by 100 and so on.

5) Subtract the equation formed by step 2 and step 4.

6) Then find the value of x in the simplest form.

_ Express 0.2 in p / q form. |

Let x = 0.2222 ------> (1)

Multiply equation (1) by 10 as there is only one number is repeating.

10 x = 2.2222 ------> (2)

Subtract equation (1) from (2)

9x = 2 ( dividing both side by 9)

x = 2 / 9

___ Express 0.585 in p / q form. |

As there is bar on three digits, so multiply equation by 1000.

1000 x = 585.585585 ------------> (2)

Subtract equation (1) from (2), we get

999 x = 585

x = 585 / 999 ( dividing both sides by 999)

x = 65 / 111 ( writing it in lowest form)

_ Express 0.123 in p / q form. |

As there is a bar on one digit so multiply equation (1) by 10

10 x = 12.333 --------------> (2)

Subtract equation (1) from (2)

9 x = 1.11

x = 1.11 / 9

x = 111 / 900

• Representation of rational number on number line

• Comparison of rational number

• Addition rational numbers

• Subtraction of rational numbers

• Conversion of rational numbers to decimals

• Irrational Numbers

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