0.123 (1 And 3 Repeating) As A Fraction

2 min read Jul 05, 2024

0.123 (1 and 3 repeating) as a Fraction

In decimal notation, the number 0.123 with the digits 1 and 3 repeating indefinitely can be written as 0.12341234... . This repeating decimal can be converted to a fraction, which is a more compact and useful way to express the number.

Converting the Repeating Decimal to a Fraction

To convert the repeating decimal 0.12341234... to a fraction, we can use the following steps:

Step 1: Let x = 0.12341234...

Let x be equal to the repeating decimal 0.12341234... .

Step 2: Multiply x by 1000

Multiply both sides of the equation by 1000 to get:

1000x = 123.12341234...

Step 3: Subtract x from 1000x

Subtract x from both sides of the equation to get:

999x = 123

Step 4: Solve for x

Divide both sides of the equation by 999 to solve for x:

x = 123/999

Step 5: Simplify the Fraction

Simplify the fraction 123/999 by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

x = 41/333

Result

The repeating decimal 0.12341234... can be converted to the fraction:

41/333

This fraction is a more compact and useful way to express the number, and it can be used in various mathematical operations and applications.

0.123 (1 And 3 Repeating) As A Fraction