Writing Pure Recurring Decimal into Rational Number Form

Pure recurring decimals are those decimals in which all the digits after the decimal point are repeating.

Examples:

pure recursive

In this section we will look at the methods to write these decimals into rational number form i.e. the fraction form.

Writing Recurring Decimal into Fractional Form

We will take a look at the method with an example.

$Conversion of decimal into fraction$

Hence in this way we can convert a pure recurring decimal into a rational number form.

1. Remove the decimal point and write the recurring digits as the numerator

2. In the denominator write as many nines as the recurring digits.

3. Finally, write the fraction in its lowest form.

Examples:

Convert the given recurring decimal into rational form :

1. 0.252525………………

Using step 1 we get numerator = 25

Using step 2 since two digits i.e. 25 are repeating, denominator = 99

Hence 0.252525…… $$= \frac{25}{99}$$

2. 0.33……………..

Again using the above steps we get:

0.333…… $$= \frac{3}{9}$$ $$= \frac{1}{3}$$ (Reducing to its lowest form)

3. 0.243243243….. $$ =\frac{243}{999}$$ $$ =\frac{27}{111}$$ $$= \frac{9}{37}$$

Help with Grade 8Number Sense, Help with writing Decimal to Number Form, how to write Decimal to Number Form