Question

how to convert a rational number into decimal

Answer 1

Answer:

There are two types of rational no.

• finite or terminating decimal
• Non terminating decimals.

Finite or terminating decimals :

The rational no. with a finite decimal part or for which the long division terminates ( stops) after a definite number of steps are known as finite or terminating decimals.

Example 1:

• Express 7 / 8 rational numbers to decimals form by long division method.
• 7 / 8 = 0.875

Example 2:

• Express - 17 / 8 in the decimal form by long division method.
• - 17 / 8 = - 2.125

Non terminating decimals :

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

Example 1:

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

Example 2:

Express 0.585 in p / q form.

Let x = 0.585585585 --------> (1)

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)

hope it helps you ♥✌️⚡

Answer 2

Answer:

The decimal forms of rational numbers either and or repeat a pattern . To convert fractions to decimals you just divide the top by the bottom - divide the numerator by the denominator - and if the division doesn't come out evenly , you can stop after a certain number of decimal places and round off .